Daily Papers

Deep neural networks have achieved remarkable progress in enhancing low-light images by improving their brightness and eliminating noise. However, most existing methods construct end-to-end mapping networks heuristically, neglecting the intrinsic prior of image enhancement task and lacking transparency and interpretability. Although some unfolding solutions have been proposed to relieve these issues, they rely on proximal operator networks that deliver ambiguous and implicit priors. In this work, we propose a paradigm for low-light image enhancement that explores the potential of customized learnable priors to improve the transparency of the deep unfolding paradigm. Motivated by the powerful feature representation capability of Masked Autoencoder (MAE), we customize MAE-based illumination and noise priors and redevelop them from two perspectives: 1) structure flow: we train the MAE from a normal-light image to its illumination properties and then embed it into the proximal operator design of the unfolding architecture; and m2) optimization flow: we train MAE from a normal-light image to its gradient representation and then employ it as a regularization term to constrain noise in the model output. These designs improve the interpretability and representation capability of the model.Extensive experiments on multiple low-light image enhancement datasets demonstrate the superiority of our proposed paradigm over state-of-the-art methods. Code is available at https://github.com/zheng980629/CUE.

Pre-trained models for programming language have achieved dramatic empirical improvements on a variety of code-related tasks such as code search, code completion, code summarization, etc. However, existing pre-trained models regard a code snippet as a sequence of tokens, while ignoring the inherent structure of code, which provides crucial code semantics and would enhance the code understanding process. We present GraphCodeBERT, a pre-trained model for programming language that considers the inherent structure of code. Instead of taking syntactic-level structure of code like abstract syntax tree (AST), we use data flow in the pre-training stage, which is a semantic-level structure of code that encodes the relation of "where-the-value-comes-from" between variables. Such a semantic-level structure is neat and does not bring an unnecessarily deep hierarchy of AST, the property of which makes the model more efficient. We develop GraphCodeBERT based on Transformer. In addition to using the task of masked language modeling, we introduce two structure-aware pre-training tasks. One is to predict code structure edges, and the other is to align representations between source code and code structure. We implement the model in an efficient way with a graph-guided masked attention function to incorporate the code structure. We evaluate our model on four tasks, including code search, clone detection, code translation, and code refinement. Results show that code structure and newly introduced pre-training tasks can improve GraphCodeBERT and achieves state-of-the-art performance on the four downstream tasks. We further show that the model prefers structure-level attentions over token-level attentions in the task of code search.

Image inpainting techniques have shown significant improvements by using deep neural networks recently. However, most of them may either fail to reconstruct reasonable structures or restore fine-grained textures. In order to solve this problem, in this paper, we propose a two-stage model which splits the inpainting task into two parts: structure reconstruction and texture generation. In the first stage, edge-preserved smooth images are employed to train a structure reconstructor which completes the missing structures of the inputs. In the second stage, based on the reconstructed structures, a texture generator using appearance flow is designed to yield image details. Experiments on multiple publicly available datasets show the superior performance of the proposed network.

Recent flow matching models for text-to-image generation have achieved remarkable quality, yet their integration with reinforcement learning for human preference alignment remains suboptimal, hindering fine-grained reward-based optimization. We observe that the key impediment to effective GRPO training of flow models is the temporal uniformity assumption in existing approaches: sparse terminal rewards with uniform credit assignment fail to capture the varying criticality of decisions across generation timesteps, resulting in inefficient exploration and suboptimal convergence. To remedy this shortcoming, we introduce TempFlow-GRPO (Temporal Flow GRPO), a principled GRPO framework that captures and exploits the temporal structure inherent in flow-based generation. TempFlow-GRPO introduces two key innovations: (i) a trajectory branching mechanism that provides process rewards by concentrating stochasticity at designated branching points, enabling precise credit assignment without requiring specialized intermediate reward models; and (ii) a noise-aware weighting scheme that modulates policy optimization according to the intrinsic exploration potential of each timestep, prioritizing learning during high-impact early stages while ensuring stable refinement in later phases. These innovations endow the model with temporally-aware optimization that respects the underlying generative dynamics, leading to state-of-the-art performance in human preference alignment and standard text-to-image benchmarks.

Structure-Based molecule optimization (SBMO) aims to optimize molecules with both continuous coordinates and discrete types against protein targets. A promising direction is to exert gradient guidance on generative models given its remarkable success in images, but it is challenging to guide discrete data and risks inconsistencies between modalities. To this end, we leverage a continuous and differentiable space derived through Bayesian inference, presenting Molecule Joint Optimization (MolJO), the gradient-based SBMO framework that facilitates joint guidance signals across different modalities while preserving SE(3)-equivariance. We introduce a novel backward correction strategy that optimizes within a sliding window of the past histories, allowing for a seamless trade-off between explore-and-exploit during optimization. MolJO achieves state-of-the-art performance on CrossDocked2020 benchmark (Success Rate 51.3%, Vina Dock -9.05 and SA 0.78), more than 4x improvement in Success Rate compared to the gradient-based counterpart, and 2x "Me-Better" Ratio as much as 3D baselines. Furthermore, we extend MolJO to a wide range of optimization settings, including multi-objective optimization and challenging tasks in drug design such as R-group optimization and scaffold hopping, further underscoring its versatility. Code is available at https://github.com/AlgoMole/MolCRAFT.

Different from the flow semantics of natural languages, programming languages are inherently rigid in structure and grammar. Existing fine-tuning methodologies for code vulnerability detection generally treat code as long text sequences, stripping away structural elements such as newlines ('/n') and whitespace. However, this approach inadvertently results in the loss of crucial structural information, diminishing the distinct characteristics of code and impairing the accuracy of vulnerability detection. To address these challenges, we propose a novel network architecture method based on pre-trained code models, which incorporates structural information awareness. We propose an enhanced code text processing workflow that retains structural elements prior to modeling. This refinement allows the model to retain and exploit line-level structural information and semantic information during the modeling process. Furthermore, we introduce a new network architecture, the Code Structure-Aware Network through Line-level Semantic Learning (CSLS), which integrates three key components: global vulnerability awareness, line-structural awareness, and sensitive-line awareness. We have conducted comprehensive experiments using vulnerability detection datasets from real-world projects. Extensive experiments were conducted on vulnerability detection datasets derived from real-world projects. The results demonstrate that our new code pre-processing flow significantly improves existing baselines (e.g., a 3\% accuracy improvement on the Devign dataset when applied to popular models such as CoderBert and UniXcoder). The proposed network architecture also demonstrates superior accuracy in detecting vulnerabilities, surpassing newly established benchmarks. These findings underscore the importance of structural information in enhancing the efficacy of code vulnerability detection models.

Text-to-video diffusion models are notoriously limited in their ability to model temporal aspects such as motion, physics, and dynamic interactions. Existing approaches address this limitation by retraining the model or introducing external conditioning signals to enforce temporal consistency. In this work, we explore whether a meaningful temporal representation can be extracted directly from the predictions of a pre-trained model without any additional training or auxiliary inputs. We introduce FlowMo, a novel training-free guidance method that enhances motion coherence using only the model's own predictions in each diffusion step. FlowMo first derives an appearance-debiased temporal representation by measuring the distance between latents corresponding to consecutive frames. This highlights the implicit temporal structure predicted by the model. It then estimates motion coherence by measuring the patch-wise variance across the temporal dimension and guides the model to reduce this variance dynamically during sampling. Extensive experiments across multiple text-to-video models demonstrate that FlowMo significantly improves motion coherence without sacrificing visual quality or prompt alignment, offering an effective plug-and-play solution for enhancing the temporal fidelity of pre-trained video diffusion models.

Flowcharts are a critical tool for visualizing decision-making processes. However, their non-linear structure and complex visual-textual relationships make it challenging to interpret them using LLMs, as vision-language models frequently hallucinate nonexistent connections and decision paths when analyzing these diagrams. This leads to compromised reliability for automated flowchart processing in critical domains such as logistics, health, and engineering. We introduce the task of Fine-grained Flowchart Attribution, which traces specific components grounding a flowchart referring LLM response. Flowchart Attribution ensures the verifiability of LLM predictions and improves explainability by linking generated responses to the flowchart's structure. We propose FlowPathAgent, a neurosymbolic agent that performs fine-grained post hoc attribution through graph-based reasoning. It first segments the flowchart, then converts it into a structured symbolic graph, and then employs an agentic approach to dynamically interact with the graph, to generate attribution paths. Additionally, we present FlowExplainBench, a novel benchmark for evaluating flowchart attributions across diverse styles, domains, and question types. Experimental results show that FlowPathAgent mitigates visual hallucinations in LLM answers over flowchart QA, outperforming strong baselines by 10-14% on our proposed FlowExplainBench dataset.

In this work, we propose WaveFlow, a small-footprint generative flow for raw audio, which is directly trained with maximum likelihood. It handles the long-range structure of 1-D waveform with a dilated 2-D convolutional architecture, while modeling the local variations using expressive autoregressive functions. WaveFlow provides a unified view of likelihood-based models for 1-D data, including WaveNet and WaveGlow as special cases. It generates high-fidelity speech as WaveNet, while synthesizing several orders of magnitude faster as it only requires a few sequential steps to generate very long waveforms with hundreds of thousands of time-steps. Furthermore, it can significantly reduce the likelihood gap that has existed between autoregressive models and flow-based models for efficient synthesis. Finally, our small-footprint WaveFlow has only 5.91M parameters, which is 15times smaller than WaveGlow. It can generate 22.05 kHz high-fidelity audio 42.6times faster than real-time (at a rate of 939.3 kHz) on a V100 GPU without engineered inference kernels.

Generative modeling of crystal data distribution is an important yet challenging task due to the unique periodic physical symmetry of crystals. Diffusion-based methods have shown early promise in modeling crystal distribution. More recently, Bayesian Flow Networks were introduced to aggregate noisy latent variables, resulting in a variance-reduced parameter space that has been shown to be advantageous for modeling Euclidean data distributions with structural constraints (Song et al., 2023). Inspired by this, we seek to unlock its potential for modeling variables located in non-Euclidean manifolds e.g. those within crystal structures, by overcoming challenging theoretical issues. We introduce CrysBFN, a novel crystal generation method by proposing a periodic Bayesian flow, which essentially differs from the original Gaussian-based BFN by exhibiting non-monotonic entropy dynamics. To successfully realize the concept of periodic Bayesian flow, CrysBFN integrates a new entropy conditioning mechanism and empirically demonstrates its significance compared to time-conditioning. Extensive experiments over both crystal ab initio generation and crystal structure prediction tasks demonstrate the superiority of CrysBFN, which consistently achieves new state-of-the-art on all benchmarks. Surprisingly, we found that CrysBFN enjoys a significant improvement in sampling efficiency, e.g., ~100x speedup 10 v.s. 2000 steps network forwards) compared with previous diffusion-based methods on MP-20 dataset. Code is available at https://github.com/wu-han-lin/CrysBFN.

Crystalline materials are a fundamental component in next-generation technologies, yet modeling their distribution presents unique computational challenges. Of the plausible arrangements of atoms in a periodic lattice only a vanishingly small percentage are thermodynamically stable, which is a key indicator of the materials that can be experimentally realized. Two fundamental tasks in this area are to (a) predict the stable crystal structure of a known composition of elements and (b) propose novel compositions along with their stable structures. We present FlowMM, a pair of generative models that achieve state-of-the-art performance on both tasks while being more efficient and more flexible than competing methods. We generalize Riemannian Flow Matching to suit the symmetries inherent to crystals: translation, rotation, permutation, and periodic boundary conditions. Our framework enables the freedom to choose the flow base distributions, drastically simplifying the problem of learning crystal structures compared with diffusion models. In addition to standard benchmarks, we validate FlowMM's generated structures with quantum chemistry calculations, demonstrating that it is about 3x more efficient, in terms of integration steps, at finding stable materials compared to previous open methods.

This paper presents WALDO (WArping Layer-Decomposed Objects), a novel approach to the prediction of future video frames from past ones. Individual images are decomposed into multiple layers combining object masks and a small set of control points. The layer structure is shared across all frames in each video to build dense inter-frame connections. Complex scene motions are modeled by combining parametric geometric transformations associated with individual layers, and video synthesis is broken down into discovering the layers associated with past frames, predicting the corresponding transformations for upcoming ones and warping the associated object regions accordingly, and filling in the remaining image parts. Extensive experiments on multiple benchmarks including urban videos (Cityscapes and KITTI) and videos featuring nonrigid motions (UCF-Sports and H3.6M), show that our method consistently outperforms the state of the art by a significant margin in every case. Code, pretrained models, and video samples synthesized by our approach can be found in the project webpage https://16lemoing.github.io/waldo.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Diffusion models have revolutionized the field of content synthesis and editing. Recent models have replaced the traditional UNet architecture with the Diffusion Transformer (DiT), and employed flow-matching for improved training and sampling. However, they exhibit limited generation diversity. In this work, we leverage this limitation to perform consistent image edits via selective injection of attention features. The main challenge is that, unlike the UNet-based models, DiT lacks a coarse-to-fine synthesis structure, making it unclear in which layers to perform the injection. Therefore, we propose an automatic method to identify "vital layers" within DiT, crucial for image formation, and demonstrate how these layers facilitate a range of controlled stable edits, from non-rigid modifications to object addition, using the same mechanism. Next, to enable real-image editing, we introduce an improved image inversion method for flow models. Finally, we evaluate our approach through qualitative and quantitative comparisons, along with a user study, and demonstrate its effectiveness across multiple applications. The project page is available at https://omriavrahami.com/stable-flow

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead velocity, streamlines, which are also pathlines in this frame, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connecting the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, a novel formulation of the viscoelastic stress term in the momentum transport equation proposes a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that unifies semantic segmentation, classification, and image generation within a single model. Using a symmetric learning objective, SymmFlow models forward and reverse transformations jointly, ensuring bi-directional consistency, while preserving sufficient entropy for generative diversity. A new training objective is introduced to explicitly retain semantic information across flows, featuring efficient sampling while preserving semantic structure, allowing for one-step segmentation and classification without iterative refinement. Unlike previous approaches that impose strict one-to-one mapping between masks and images, SymmFlow generalizes to flexible conditioning, supporting both pixel-level and image-level class labels. Experimental results on various benchmarks demonstrate that SymmFlow achieves state-of-the-art performance on semantic image synthesis, obtaining FID scores of 11.9 on CelebAMask-HQ and 7.0 on COCO-Stuff with only 25 inference steps. Additionally, it delivers competitive results on semantic segmentation and shows promising capabilities in classification tasks. The code will be publicly available.

Diffusion models achieve strong generative performance but often rely on large datasets that may include sensitive content. This challenge is compounded by the models' tendency to memorize training data, raising privacy concerns. SFBD (Lu et al., 2025) addresses this by training on corrupted data and using limited clean samples to capture local structure and improve convergence. However, its iterative denoising and fine-tuning loop requires manual coordination, making it burdensome to implement. We reinterpret SFBD as an alternating projection algorithm and introduce a continuous variant, SFBD flow, that removes the need for alternating steps. We further show its connection to consistency constraint-based methods, and demonstrate that its practical instantiation, Online SFBD, consistently outperforms strong baselines across benchmarks.

Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on irregular or unstructured data like 3D point clouds or even protein structures. These models are commonly trained in two stages: first, a data compressor is trained, and in a subsequent training stage a flow matching generative model is trained in the latent space of the data compressor. This two-stage paradigm sets obstacles for unifying models across data domains, as hand-crafted compressors architectures are used for different data modalities. To this end, we introduce INRFlow, a domain-agnostic approach to learn flow matching transformers directly in ambient space. Drawing inspiration from INRs, we introduce a conditionally independent point-wise training objective that enables INRFlow to make predictions continuously in coordinate space. Our empirical results demonstrate that INRFlow effectively handles different data modalities such as images, 3D point clouds and protein structure data, achieving strong performance in different domains and outperforming comparable approaches. INRFlow is a promising step towards domain-agnostic flow matching generative models that can be trivially adopted in different data domains.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Unsupervised anomaly detection (UAD) in brain imaging is crucial for identifying pathologies without the need for labeled data. However, accurately localizing anomalies remains challenging due to the intricate structure of brain anatomy and the scarcity of abnormal examples. In this work, we introduce REFLECT, a novel framework that leverages rectified flows to establish a direct, linear trajectory for correcting abnormal MR images toward a normal distribution. By learning a straight, one-step correction transport map, our method efficiently corrects brain anomalies and can precisely localize anomalies by detecting discrepancies between anomalous input and corrected counterpart. In contrast to the diffusion-based UAD models, which require iterative stochastic sampling, rectified flows provide a direct transport map, enabling single-step inference. Extensive experiments on popular UAD brain segmentation benchmarks demonstrate that REFLECT significantly outperforms state-of-the-art unsupervised anomaly detection methods. The code is available at https://github.com/farzad-bz/REFLECT.

Autoregressive (AR) modeling has achieved remarkable success in natural language processing by enabling models to generate text with coherence and contextual understanding through next token prediction. Recently, in image generation, VAR proposes scale-wise autoregressive modeling, which extends the next token prediction to the next scale prediction, preserving the 2D structure of images. However, VAR encounters two primary challenges: (1) its complex and rigid scale design limits generalization in next scale prediction, and (2) the generator's dependence on a discrete tokenizer with the same complex scale structure restricts modularity and flexibility in updating the tokenizer. To address these limitations, we introduce FlowAR, a general next scale prediction method featuring a streamlined scale design, where each subsequent scale is simply double the previous one. This eliminates the need for VAR's intricate multi-scale residual tokenizer and enables the use of any off-the-shelf Variational AutoEncoder (VAE). Our simplified design enhances generalization in next scale prediction and facilitates the integration of Flow Matching for high-quality image synthesis. We validate the effectiveness of FlowAR on the challenging ImageNet-256 benchmark, demonstrating superior generation performance compared to previous methods. Codes will be available at https://github.com/OliverRensu/FlowAR.

The alignment between RNA sequences and structures in foundation models (FMs) has yet to be thoroughly investigated. Existing FMs have struggled to establish sequence-structure alignment, hindering the free flow of genomic information between RNA sequences and structures. In this study, we introduce OmniGenome, an RNA FM trained to align RNA sequences with respect to secondary structures based on structure-contextualised modelling. The alignment enables free and bidirectional mappings between sequences and structures by utilising the flexible RNA modelling paradigm that supports versatile input and output modalities, i.e., sequence and/or structure as input/output. We implement RNA design and zero-shot secondary structure prediction as case studies to evaluate the Seq2Str and Str2Seq mapping capacity of OmniGenome. Results on the EternaV2 benchmark show that OmniGenome solved 74% of puzzles, whereas existing FMs only solved up to 3% of the puzzles due to the oversight of sequence-structure alignment. We leverage four comprehensive in-silico genome modelling benchmarks to evaluate performance across a diverse set of genome downstream tasks, where the results show that OmniGenome achieves state-of-the-art performance on RNA and DNA benchmarks, even without any training on DNA genomes.

Reliable high-definition (HD) map construction is crucial for the driving safety of autonomous vehicles. Although recent studies demonstrate improved performance, their generalization capability across unfamiliar driving scenes remains unexplored. To tackle this issue, we propose UIGenMap, an uncertainty-instructed structure injection approach for generalizable HD map vectorization, which concerns the uncertainty resampling in statistical distribution and employs explicit instance features to reduce excessive reliance on training data. Specifically, we introduce the perspective-view (PV) detection branch to obtain explicit structural features, in which the uncertainty-aware decoder is designed to dynamically sample probability distributions considering the difference in scenes. With probabilistic embedding and selection, UI2DPrompt is proposed to construct PV-learnable prompts. These PV prompts are integrated into the map decoder by designed hybrid injection to compensate for neglected instance structures. To ensure real-time inference, a lightweight Mimic Query Distillation is designed to learn from PV prompts, which can serve as an efficient alternative to the flow of PV branches. Extensive experiments on challenging geographically disjoint (geo-based) data splits demonstrate that our UIGenMap achieves superior performance, with +5.7 mAP improvement on the nuScenes dataset. Source code will be available at https://github.com/xiaolul2/UIGenMap.

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data.

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few global basis. The proposed approach is successfully demonstrated for the reduction of several simple but representative problems.

Text-to-image (T2I) diffusion/flow models have drawn considerable attention recently due to their remarkable ability to deliver flexible visual creations. Still, high-resolution image synthesis presents formidable challenges due to the scarcity and complexity of high-resolution content. To this end, we present HiFlow, a training-free and model-agnostic framework to unlock the resolution potential of pre-trained flow models. Specifically, HiFlow establishes a virtual reference flow within the high-resolution space that effectively captures the characteristics of low-resolution flow information, offering guidance for high-resolution generation through three key aspects: initialization alignment for low-frequency consistency, direction alignment for structure preservation, and acceleration alignment for detail fidelity. By leveraging this flow-aligned guidance, HiFlow substantially elevates the quality of high-resolution image synthesis of T2I models and demonstrates versatility across their personalized variants. Extensive experiments validate HiFlow's superiority in achieving superior high-resolution image quality over current state-of-the-art methods.

Scene flow estimation aims to recover per-point motion from two adjacent LiDAR scans. However, in real-world applications such as autonomous driving, points rarely move independently of others, especially for nearby points belonging to the same object, which often share the same motion. Incorporating this locally rigid motion constraint has been a key challenge in self-supervised scene flow estimation, which is often addressed by post-processing or appending extra regularization. While these approaches are able to improve the rigidity of predicted flows, they lack an architectural inductive bias for local rigidity within the model structure, leading to suboptimal learning efficiency and inferior performance. In contrast, we enforce local rigidity with a lightweight add-on module in neural network design, enabling end-to-end learning. We design a discretized voting space that accommodates all possible translations and then identify the one shared by nearby points by differentiable voting. Additionally, to ensure computational efficiency, we operate on pillars rather than points and learn representative features for voting per pillar. We plug the Voting Module into popular model designs and evaluate its benefit on Argoverse 2 and Waymo datasets. We outperform baseline works with only marginal compute overhead. Code is available at https://github.com/tudelft-iv/VoteFlow.

Peptides, short chains of amino acid residues, play a vital role in numerous biological processes by interacting with other target molecules, offering substantial potential in drug discovery. In this work, we present PepFlow, the first multi-modal deep generative model grounded in the flow-matching framework for the design of full-atom peptides that target specific protein receptors. Drawing inspiration from the crucial roles of residue backbone orientations and side-chain dynamics in protein-peptide interactions, we characterize the peptide structure using rigid backbone frames within the SE(3) manifold and side-chain angles on high-dimensional tori. Furthermore, we represent discrete residue types in the peptide sequence as categorical distributions on the probability simplex. By learning the joint distributions of each modality using derived flows and vector fields on corresponding manifolds, our method excels in the fine-grained design of full-atom peptides. Harnessing the multi-modal paradigm, our approach adeptly tackles various tasks such as fix-backbone sequence design and side-chain packing through partial sampling. Through meticulously crafted experiments, we demonstrate that PepFlow exhibits superior performance in comprehensive benchmarks, highlighting its significant potential in computational peptide design and analysis.

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the U(1) degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous U(1) system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Accurately detecting rice flowering time is crucial for timely pollination in hybrid rice seed production. This not only enhances pollination efficiency but also ensures higher yields. However, due to the complexity of field environments and the characteristics of rice spikelets, such as their small size and short flowering period, automated and precise recognition remains challenging. To address this, this study proposes a rice spikelet flowering recognition method based on an improved YOLOv8 object detection model. First, a Bidirectional Feature Pyramid Network (BiFPN) replaces the original PANet structure to enhance feature fusion and improve multi-scale feature utilization. Second, to boost small object detection, a p2 small-object detection head is added, using finer feature mapping to reduce feature loss commonly seen in detecting small targets. Given the lack of publicly available datasets for rice spikelet flowering in field conditions, a high-resolution RGB camera and data augmentation techniques are used to construct a dedicated dataset, providing reliable support for model training and testing. Experimental results show that the improved YOLOv8s-p2 model achieves an mAP@0.5 of 65.9%, precision of 67.6%, recall of 61.5%, and F1-score of 64.41%, representing improvements of 3.10%, 8.40%, 10.80%, and 9.79%, respectively, over the baseline YOLOv8. The model also runs at 69 f/s on the test set, meeting practical application requirements. Overall, the improved YOLOv8s-p2 offers high accuracy and speed, providing an effective solution for automated monitoring in hybrid rice seed production.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Biological processes, functions, and properties are intricately linked to the ensemble of protein conformations, rather than being solely determined by a single stable conformation. In this study, we have developed P2DFlow, a generative model based on SE(3) flow matching, to predict the structural ensembles of proteins. We specifically designed a valuable prior for the flow process and enhanced the model's ability to distinguish each intermediate state by incorporating an additional dimension to describe the ensemble data, which can reflect the physical laws governing the distribution of ensembles, so that the prior knowledge can effectively guide the generation process. When trained and evaluated on the MD datasets of ATLAS, P2DFlow outperforms other baseline models on extensive experiments, successfully capturing the observable dynamic fluctuations as evidenced in crystal structure and MD simulations. As a potential proxy agent for protein molecular simulation, the high-quality ensembles generated by P2DFlow could significantly aid in understanding protein functions across various scenarios. Code is available at https://github.com/BLEACH366/P2DFlow

Selective state space models (SSMs), such as Mamba, highly excel at capturing long-range dependencies in 1D sequential data, while their applications to 2D vision tasks still face challenges. Current visual SSMs often convert images into 1D sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood connectivity directly in the state space. Instead of relying solely on sequential state transitions, we introduce a structure-aware state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation using the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multiplication framework, providing a deeper understanding of our method. Experimental results demonstrate that Spatial-Mamba, even with a single scan, attains or surpasses the state-of-the-art SSM-based models in image classification, detection and segmentation. Source codes and trained models can be found at https://github.com/EdwardChasel/Spatial-Mamba.

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are probabilistic models, and may be expressed in the language of graphical models with random variables whose values are complex data types such as strings. Cases with control flow and dynamic structure require techniques from probabilistic programming, which allow implementing disparate model structures and inference strategies in a unified language. We formalize several existing techniques from this perspective, including scratchpads / chain of thought, verifiers, STaR, selection-inference, and tool use. We refer to the resulting programs as language model cascades.

Deep convolutional neural networks perform better on images containing spatially invariant noise (synthetic noise); however, their performance is limited on real-noisy photographs and requires multiple stage network modeling. To advance the practicability of denoising algorithms, this paper proposes a novel single-stage blind real image denoising network (RIDNet) by employing a modular architecture. We use a residual on the residual structure to ease the flow of low-frequency information and apply feature attention to exploit the channel dependencies. Furthermore, the evaluation in terms of quantitative metrics and visual quality on three synthetic and four real noisy datasets against 19 state-of-the-art algorithms demonstrate the superiority of our RIDNet.

Super-Resolution convolutional neural networks have recently demonstrated high-quality restoration for single images. However, existing algorithms often require very deep architectures and long training times. Furthermore, current convolutional neural networks for super-resolution are unable to exploit features at multiple scales and weigh them equally, limiting their learning capability. In this exposition, we present a compact and accurate super-resolution algorithm namely, Densely Residual Laplacian Network (DRLN). The proposed network employs cascading residual on the residual structure to allow the flow of low-frequency information to focus on learning high and mid-level features. In addition, deep supervision is achieved via the densely concatenated residual blocks settings, which also helps in learning from high-level complex features. Moreover, we propose Laplacian attention to model the crucial features to learn the inter and intra-level dependencies between the feature maps. Furthermore, comprehensive quantitative and qualitative evaluations on low-resolution, noisy low-resolution, and real historical image benchmark datasets illustrate that our DRLN algorithm performs favorably against the state-of-the-art methods visually and accurately.

Program source code contains complex structure information, which can be represented in structured data forms like trees or graphs. To acquire the structural information in source code, most existing researches use abstract syntax trees (AST). A group of works add additional edges to ASTs to convert source code into graphs and use graph neural networks to learn representations for program graphs. Although these works provide additional control or data flow information to ASTs for downstream tasks, they neglect an important aspect of structure information in AST itself: the different types of nodes and edges. In ASTs, different nodes contain different kinds of information like variables or control flow, and the relation between a node and all its children can also be different. To address the information of node and edge types, we bring the idea of heterogeneous graphs to learning on source code and present a new formula of building heterogeneous program graphs from ASTs with additional type information for nodes and edges. We use the ASDL grammar of programming language to define the node and edge types of program graphs. Then we use heterogeneous graph neural networks to learn on these graphs. We evaluate our approach on two tasks: code comment generation and method naming. Both tasks require reasoning on the semantics of complete code snippets. Experiment results show that our approach outperforms baseline models, including homogeneous graph-based models, showing that leveraging the type information of nodes and edges in program graphs can help in learning program semantics.

We propose a new end-to-end single image dehazing method, called Densely Connected Pyramid Dehazing Network (DCPDN), which can jointly learn the transmission map, atmospheric light and dehazing all together. The end-to-end learning is achieved by directly embedding the atmospheric scattering model into the network, thereby ensuring that the proposed method strictly follows the physics-driven scattering model for dehazing. Inspired by the dense network that can maximize the information flow along features from different levels, we propose a new edge-preserving densely connected encoder-decoder structure with multi-level pyramid pooling module for estimating the transmission map. This network is optimized using a newly introduced edge-preserving loss function. To further incorporate the mutual structural information between the estimated transmission map and the dehazed result, we propose a joint-discriminator based on generative adversarial network framework to decide whether the corresponding dehazed image and the estimated transmission map are real or fake. An ablation study is conducted to demonstrate the effectiveness of each module evaluated at both estimated transmission map and dehazed result. Extensive experiments demonstrate that the proposed method achieves significant improvements over the state-of-the-art methods. Code will be made available at: https://github.com/hezhangsprinter

The creation of 3D assets with explicit, editable part structures is crucial for advancing interactive applications, yet most generative methods produce only monolithic shapes, limiting their utility. We introduce OmniPart, a novel framework for part-aware 3D object generation designed to achieve high semantic decoupling among components while maintaining robust structural cohesion. OmniPart uniquely decouples this complex task into two synergistic stages: (1) an autoregressive structure planning module generates a controllable, variable-length sequence of 3D part bounding boxes, critically guided by flexible 2D part masks that allow for intuitive control over part decomposition without requiring direct correspondences or semantic labels; and (2) a spatially-conditioned rectified flow model, efficiently adapted from a pre-trained holistic 3D generator, synthesizes all 3D parts simultaneously and consistently within the planned layout. Our approach supports user-defined part granularity, precise localization, and enables diverse downstream applications. Extensive experiments demonstrate that OmniPart achieves state-of-the-art performance, paving the way for more interpretable, editable, and versatile 3D content.

Current instruction data synthesis methods primarily focus on single-turn instructions and often neglect cross-turn coherence, resulting in context drift and reduced task completion rates in extended conversations. To address this limitation, we propose Skeleton-Guided Multi-Turn Dialogue Generation, a framework that constrains multi-turn instruction synthesis by explicitly modeling human conversational intent. It operates in two stages: (1) Intent Modeling, which captures the global structure of human dialogues by assigning each conversation to one of nine well-defined intent trajectories, ensuring a coherent and goal-oriented information flow; and (2) Skeleton Generation, which constructs a structurally grounded sequence of user queries aligned with the modeled intent, thereby serving as a scaffold that constrains and guides the downstream instruction synthesis process. Based on this process, we construct ConsistentChat, a multi-turn instruction dataset with approximately 15,000 multi-turn conversations and 224,392 utterances. Experiments on the Light, Topdial, and MT-Eval benchmarks show that models fine-tuned on ConsistentChat achieve a 20-30% improvement in chat consistency and up to a 15% increase in task success rate, significantly outperforming models trained on existing single-turn and multi-turn instruction datasets.

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-B\'enard convection, we found CoDA-NO to outperform existing methods by over 36%.

Visual motion processing is essential for humans to perceive and interact with dynamic environments. Despite extensive research in cognitive neuroscience, image-computable models that can extract informative motion flow from natural scenes in a manner consistent with human visual processing have yet to be established. Meanwhile, recent advancements in computer vision (CV), propelled by deep learning, have led to significant progress in optical flow estimation, a task closely related to motion perception. Here we propose an image-computable model of human motion perception by bridging the gap between biological and CV models. Specifically, we introduce a novel two-stages approach that combines trainable motion energy sensing with a recurrent self-attention network for adaptive motion integration and segregation. This model architecture aims to capture the computations in V1-MT, the core structure for motion perception in the biological visual system, while providing the ability to derive informative motion flow for a wide range of stimuli, including complex natural scenes. In silico neurophysiology reveals that our model's unit responses are similar to mammalian neural recordings regarding motion pooling and speed tuning. The proposed model can also replicate human responses to a range of stimuli examined in past psychophysical studies. The experimental results on the Sintel benchmark demonstrate that our model predicts human responses better than the ground truth, whereas the state-of-the-art CV models show the opposite. Our study provides a computational architecture consistent with human visual motion processing, although the physiological correspondence may not be exact.

Temporal motion modeling has always been a key component in multiple object tracking (MOT) which can ensure smooth trajectory movement and provide accurate positional information to enhance association precision. However, current motion models struggle to be both efficient and effective across different application scenarios. To this end, we propose TrackSSM inspired by the recently popular state space models (SSM), a unified encoder-decoder motion framework that uses data-dependent state space model to perform temporal motion of trajectories. Specifically, we propose Flow-SSM, a module that utilizes the position and motion information from historical trajectories to guide the temporal state transition of object bounding boxes. Based on Flow-SSM, we design a flow decoder. It is composed of a cascaded motion decoding module employing Flow-SSM, which can use the encoded flow information to complete the temporal position prediction of trajectories. Additionally, we propose a Step-by-Step Linear (S^2L) training strategy. By performing linear interpolation between the positions of the object in the previous frame and the current frame, we construct the pseudo labels of step-by-step linear training, ensuring that the trajectory flow information can better guide the object bounding box in completing temporal transitions. TrackSSM utilizes a simple Mamba-Block to build a motion encoder for historical trajectories, forming a temporal motion model with an encoder-decoder structure in conjunction with the flow decoder. TrackSSM is applicable to various tracking scenarios and achieves excellent tracking performance across multiple benchmarks, further extending the potential of SSM-like temporal motion models in multi-object tracking tasks. Code and models are publicly available at https://github.com/Xavier-Lin/TrackSSM.

We develop a deep reinforcement learning method for training a jellyfish-like swimmer to effectively track a moving target in a two-dimensional flow. This swimmer is a flexible object equipped with a muscle model based on torsional springs. We employ a deep Q-network (DQN) that takes the swimmer's geometry and dynamic parameters as inputs, and outputs actions which are the forces applied to the swimmer. In particular, we introduce an action regulation to mitigate the interference from complex fluid-structure interactions. The goal of these actions is to navigate the swimmer to a target point in the shortest possible time. In the DQN training, the data on the swimmer's motions are obtained from simulations conducted using the immersed boundary method. During tracking a moving target, there is an inherent delay between the application of forces and the corresponding response of the swimmer's body due to hydrodynamic interactions between the shedding vortices and the swimmer's own locomotion. Our tests demonstrate that the swimmer, with the DQN agent and action regulation, is able to dynamically adjust its course based on its instantaneous state. This work extends the application scope of machine learning in controlling flexible objects within fluid environments.

The vanilla autoregressive image generation model generates visual tokens in a step-by-step fashion, which limits the ability to capture holistic relationships among token sequences. Moreover, most visual tokenizers map local image patches into latent tokens, leading to limited global information. To address this, we introduce Hita, a novel image tokenizer for autoregressive (AR) image generation. It introduces a holistic-to-local tokenization scheme with learnable holistic queries and local patch tokens. Besides, Hita incorporates two key strategies for improved alignment with the AR generation process: 1) it arranges a sequential structure with holistic tokens at the beginning followed by patch-level tokens while using causal attention to maintain awareness of previous tokens; and 2) before feeding the de-quantized tokens into the decoder, Hita adopts a lightweight fusion module to control information flow to prioritize holistic tokens. Extensive experiments show that Hita accelerates the training speed of AR generators and outperforms those trained with vanilla tokenizers, achieving 2.59 FID and 281.9 IS on the ImageNet benchmark. A detailed analysis of the holistic representation highlights its ability to capture global image properties such as textures, materials, and shapes. Additionally, Hita also demonstrates effectiveness in zero-shot style transfer and image in-painting. The code is available at https://github.com/CVMI-Lab/Hita{https://github.com/CVMI-Lab/Hita}

This is the second part of the two-paper sequence, which aims to present a comprehensive study for current-vortex sheets with or without surface tension in ideal compressible magnetohydrodynamics (MHD). The results of this paper are two-fold: First, we establish the zero-surface-tension limit of compressible current-vortex sheets under certain stability conditions on the free interface; Second, when the two-phase flows are isentropic and the density functions converge to the same constant as Mach number goes to zero, we can drop the boundedness assumption (with respect to Mach number) on high-order time derivatives by combining the paradifferential approach applied to the evolution equation of the free interface, the structure of wave equations for the total pressure and the anisotropic Sobolev spaces with suitable weights of Mach number. To our knowledge, this is the first result that rigorously justifies the incompressible limit of free-surface MHD flows. Moreover, we actually present a robust framework for the low Mach number limit of vortex-sheet problems, which was never established in any previous works.

Multi-turn instruction following capability constitutes a core competency of large language models (LLMs) in real-world applications. Existing evaluation benchmarks predominantly focus on fine-grained constraint satisfaction and domain-specific capability assessment, yet overlook the crucial structural dependency between dialogue turns that distinguishes multi-turn from single-turn interactions. This structural dependency not only reflects user intent but also establishes a second dimension for instruction following evaluation beyond constraint satisfaction. To address this gap, we propose StructFlowBench, a multi-turn instruction following benchmark with structural flow modeling. The benchmark innovatively defines a structural flow framework comprising six fundamental inter-turn relationships, which not only introduces novel structural constraints for model evaluation but also serves as generation parameters for creating customized dialogue flows tailored to specific scenarios. Adopting established LLM-based automatic evaluation methodologies, we conduct systematic evaluations of 13 leading open-source and closed-source LLMs. Experimental results reveal significant deficiencies in current models' comprehension of multi-turn dialogue structures. The code is available at https://github.com/MLGroupJLU/StructFlowBench.

We introduce PartCrafter, the first structured 3D generative model that jointly synthesizes multiple semantically meaningful and geometrically distinct 3D meshes from a single RGB image. Unlike existing methods that either produce monolithic 3D shapes or follow two-stage pipelines, i.e., first segmenting an image and then reconstructing each segment, PartCrafter adopts a unified, compositional generation architecture that does not rely on pre-segmented inputs. Conditioned on a single image, it simultaneously denoises multiple 3D parts, enabling end-to-end part-aware generation of both individual objects and complex multi-object scenes. PartCrafter builds upon a pretrained 3D mesh diffusion transformer (DiT) trained on whole objects, inheriting the pretrained weights, encoder, and decoder, and introduces two key innovations: (1) A compositional latent space, where each 3D part is represented by a set of disentangled latent tokens; (2) A hierarchical attention mechanism that enables structured information flow both within individual parts and across all parts, ensuring global coherence while preserving part-level detail during generation. To support part-level supervision, we curate a new dataset by mining part-level annotations from large-scale 3D object datasets. Experiments show that PartCrafter outperforms existing approaches in generating decomposable 3D meshes, including parts that are not directly visible in input images, demonstrating the strength of part-aware generative priors for 3D understanding and synthesis. Code and training data will be released.

Transformer neural operators have recently become an effective approach for surrogate modeling of systems governed by partial differential equations (PDEs). In this paper, we introduce a modified implicit factorized transformer (IFactFormer-m) model which replaces the original chained factorized attention with parallel factorized attention. The IFactFormer-m model successfully performs long-term predictions for turbulent channel flow, whereas the original IFactFormer (IFactFormer-o), Fourier neural operator (FNO), and implicit Fourier neural operator (IFNO) exhibit a poor performance. Turbulent channel flows are simulated by direct numerical simulation using fine grids at friction Reynolds numbers Re_{tau}approx 180,395,590, and filtered to coarse grids for training neural operator. The neural operator takes the current flow field as input and predicts the flow field at the next time step, and long-term prediction is achieved in the posterior through an autoregressive approach. The results show that IFactFormer-m, compared to other neural operators and the traditional large eddy simulation (LES) methods including dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model, reduces prediction errors in the short term, and achieves stable and accurate long-term prediction of various statistical properties and flow structures, including the energy spectrum, mean streamwise velocity, root mean square (rms) values of fluctuating velocities, Reynolds shear stress, and spatial structures of instantaneous velocity. Moreover, the trained IFactFormer-m is much faster than traditional LES methods. By analyzing the attention kernels, we elucidate the reasons why IFactFormer-m converges faster and achieves a stable and accurate long-term prediction compared to IFactFormer-o. Code and data are available at: https://github.com/huiyu-2002/IFactFormer-m.

The goal of decompilation is to convert compiled low-level code (e.g., assembly code) back into high-level programming languages, enabling analysis in scenarios where source code is unavailable. This task supports various reverse engineering applications, such as vulnerability identification, malware analysis, and legacy software migration. The end-to-end decompile method based on large langauge models (LLMs) reduces reliance on additional tools and minimizes manual intervention due to its inherent properties. However, previous end-to-end methods often lose critical information necessary for reconstructing control flow structures and variables when processing binary files, making it challenging to accurately recover the program's logic. To address these issues, we propose the ReF Decompile method, which incorporates the following innovations: (1) The Relabelling strategy replaces jump target addresses with labels, preserving control flow clarity. (2) The Function Call strategy infers variable types and retrieves missing variable information from binary files. Experimental results on the Humaneval-Decompile Benchmark demonstrate that ReF Decompile surpasses comparable baselines and achieves state-of-the-art (SOTA) performance of 61.43%.

Deploying language models (LMs) necessitates outputs to be both high-quality and compliant with safety guidelines. Although Inference-Time Guardrails (ITG) offer solutions that shift model output distributions towards compliance, we find that current methods struggle in balancing safety with helpfulness. ITG Methods that safely address non-compliant queries exhibit lower helpfulness while those that prioritize helpfulness compromise on safety. We refer to this trade-off as the guardrail tax, analogous to the alignment tax. To address this, we propose PrimeGuard, a novel ITG method that utilizes structured control flow. PrimeGuard routes requests to different self-instantiations of the LM with varying instructions, leveraging its inherent instruction-following capabilities and in-context learning. Our tuning-free approach dynamically compiles system-designer guidelines for each query. We construct and release safe-eval, a diverse red-team safety benchmark. Extensive evaluations demonstrate that PrimeGuard, without fine-tuning, overcomes the guardrail tax by (1) significantly increasing resistance to iterative jailbreak attacks and (2) achieving state-of-the-art results in safety guardrailing while (3) matching helpfulness scores of alignment-tuned models. Extensive evaluations demonstrate that PrimeGuard, without fine-tuning, outperforms all competing baselines and overcomes the guardrail tax by improving the fraction of safe responses from 61% to 97% and increasing average helpfulness scores from 4.17 to 4.29 on the largest models, while reducing attack success rate from 100% to 8%. PrimeGuard implementation is available at https://github.com/dynamofl/PrimeGuard and safe-eval dataset is available at https://huggingface.co/datasets/dynamoai/safe_eval.

Process-driven dialogue systems, which operate under strict predefined process constraints, are essential in customer service and equipment maintenance scenarios. Although Large Language Models (LLMs) have shown remarkable progress in dialogue and reasoning, they still struggle to solve these strictly constrained dialogue tasks. To address this challenge, we construct Process Flow Dialogue (PFDial) dataset, which contains 12,705 high-quality Chinese dialogue instructions derived from 440 flowcharts containing 5,055 process nodes. Based on PlantUML specification, each UML flowchart is converted into atomic dialogue units i.e., structured five-tuples. Experimental results demonstrate that a 7B model trained with merely 800 samples, and a 0.5B model trained on total data both can surpass 90% accuracy. Additionally, the 8B model can surpass GPT-4o up to 43.88% with an average of 11.00%. We further evaluate models' performance on challenging backward transitions in process flows and conduct an in-depth analysis of various dataset formats to reveal their impact on model performance in handling decision and sequential branches. The data is released in https://github.com/KongLongGeFDU/PFDial.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

In the literature, flows produced by synthetic jets (SJ) have been studied extensively through experiments and numeric simulations. The essential physics of such a complex system has been simplified successfully to Lumped-element models in a wide range of conditions. LE models effectively predict the pressure in the cavity and the velocity in the neck of SJ. But, this does not comprise the complete dynamics of SJ. As soon as the flow starts separating from the neck of the SJ device, vortices and jets form at some distance downstream. These structures are the result of loosening the flow boundaries. Despite such a dramatic change, predictions of LE models remain unverified by measurements of the fully developed jet. We compared predictions of momentum transfer using an LE model with measurements of size and velocity of a fully developed jet/vortex detached from an SJ. Our SJ device operated with air as an active fluid. Comparing measurements and predictions, we found a constant difference for the higher sound pressures. However, the predictions and the measurements follow similar trends. Additionally, we found that the decay rate of the flow regime given by the relationship between the Reynolds and the Strouhal numbers differs significantly when the flow is studied within the neck and downstream the cavity.

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design choice is the shape representation. An effective shape representation needs to adhere three design principles: it should allow an efficient conversion of large 3D datasets to the representation form; it should provide a good tradeoff of approximation power versus number of parameters; and it should have a simple tensorial form that is compatible with existing powerful neural architectures. While standard 3D shape representations such as volumetric grids and point clouds do not adhere to all these principles simultaneously, we advocate in this paper a new representation that does. We introduce Mosaic-SDF (M-SDF): a simple 3D shape representation that approximates the Signed Distance Function (SDF) of a given shape by using a set of local grids spread near the shape's boundary. The M-SDF representation is fast to compute for each shape individually making it readily parallelizable; it is parameter efficient as it only covers the space around the shape's boundary; and it has a simple matrix form, compatible with Transformer-based architectures. We demonstrate the efficacy of the M-SDF representation by using it to train a 3D generative flow model including class-conditioned generation with the 3D Warehouse dataset, and text-to-3D generation using a dataset of about 600k caption-shape pairs.

We present FrameFlow, a method for fast protein backbone generation using SE(3) flow matching. Specifically, we adapt FrameDiff, a state-of-the-art diffusion model, to the flow-matching generative modeling paradigm. We show how flow matching can be applied on SE(3) and propose modifications during training to effectively learn the vector field. Compared to FrameDiff, FrameFlow requires five times fewer sampling timesteps while achieving two fold better designability. The ability to generate high quality protein samples at a fraction of the cost of previous methods paves the way towards more efficient generative models in de novo protein design.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.

Finding a suitable layout represents a crucial task for diverse applications in graphic design. Motivated by simpler and smoother sampling trajectories, we explore the use of Flow Matching as an alternative to current diffusion-based layout generation models. Specifically, we propose LayoutFlow, an efficient flow-based model capable of generating high-quality layouts. Instead of progressively denoising the elements of a noisy layout, our method learns to gradually move, or flow, the elements of an initial sample until it reaches its final prediction. In addition, we employ a conditioning scheme that allows us to handle various generation tasks with varying degrees of conditioning with a single model. Empirically, LayoutFlow performs on par with state-of-the-art models while being significantly faster.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Text-guided generative diffusion models unlock powerful image creation and editing tools. While these have been extended to video generation, current approaches that edit the content of existing footage while retaining structure require expensive re-training for every input or rely on error-prone propagation of image edits across frames. In this work, we present a structure and content-guided video diffusion model that edits videos based on visual or textual descriptions of the desired output. Conflicts between user-provided content edits and structure representations occur due to insufficient disentanglement between the two aspects. As a solution, we show that training on monocular depth estimates with varying levels of detail provides control over structure and content fidelity. Our model is trained jointly on images and videos which also exposes explicit control of temporal consistency through a novel guidance method. Our experiments demonstrate a wide variety of successes; fine-grained control over output characteristics, customization based on a few reference images, and a strong user preference towards results by our model.

While recent flow-based image editing models demonstrate general-purpose capabilities across diverse tasks, they often struggle to specialize in challenging scenarios -- particularly those involving large-scale shape transformations. When performing such structural edits, these methods either fail to achieve the intended shape change or inadvertently alter non-target regions, resulting in degraded background quality. We propose Follow-Your-Shape, a training-free and mask-free framework that supports precise and controllable editing of object shapes while strictly preserving non-target content. Motivated by the divergence between inversion and editing trajectories, we compute a Trajectory Divergence Map (TDM) by comparing token-wise velocity differences between the inversion and denoising paths. The TDM enables precise localization of editable regions and guides a Scheduled KV Injection mechanism that ensures stable and faithful editing. To facilitate a rigorous evaluation, we introduce ReShapeBench, a new benchmark comprising 120 new images and enriched prompt pairs specifically curated for shape-aware editing. Experiments demonstrate that our method achieves superior editability and visual fidelity, particularly in tasks requiring large-scale shape replacement.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms na\"ive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled generation in general. In this work we introduce D-Flow, a simple framework for controlling the generation process by differentiating through the flow, optimizing for the source (noise) point. We motivate this framework by our key observation stating that for Diffusion/FM models trained with Gaussian probability paths, differentiating through the generation process projects gradient on the data manifold, implicitly injecting the prior into the optimization process. We validate our framework on linear and non-linear controlled generation problems including: image and audio inverse problems and conditional molecule generation reaching state of the art performance across all.

Using a set of LambdaCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter complexity because of reduced expressiveness of bijective mapping, which renders the models unfeasibly expensive in terms of parameters. We present an alternative parameterization scheme called NanoFlow, which uses a single neural density estimator to model multiple transformation stages. Hence, we propose an efficient parameter decomposition method and the concept of flow indication embedding, which are key missing components that enable density estimation from a single neural network. Experiments performed on audio and image models confirm that our method provides a new parameter-efficient solution for scalable NFs with significant sublinear parameter complexity.

Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: by training a network to learn only a shortcut across a probability flow, the model loses its grasp on the instantaneous velocity field that defines the flow. Our solution is to explicitly anchor the model in the underlying flow during training. We introduce the Flow-Anchored Consistency Model (FACM), a simple but effective training strategy that uses a Flow Matching (FM) task as an anchor for the primary CM shortcut objective. This Flow-Anchoring approach requires no architectural modifications and is broadly compatible with standard model architectures. By distilling a pre-trained LightningDiT model, our method achieves a state-of-the-art FID of 1.32 with two steps (NFE=2) and 1.76 with just one step (NFE=1) on ImageNet 256x256, significantly outperforming previous methods. This provides a general and effective recipe for building high-performance, few-step generative models. Our code and pretrained models: https://github.com/ali-vilab/FACM.

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can be reliably handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications. Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency. In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format. We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves state-of-the-art performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37x faster than RFDiffusion and 62x faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency. The code is available at https://github.com/AngxiaoYue/ReQFlow.

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier-Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.

Given an unconditional generative model and a predictor for a target property (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. As a highly efficient technique for steering generative models toward flexible outcomes, training-free guidance has gained increasing attention in diffusion models. However, existing methods only handle data in continuous spaces, while many scientific applications involve both continuous and discrete data (referred to as multimodality). Another emerging trend is the growing use of the simple and general flow matching framework in building generative foundation models, where guided generation remains under-explored. To address this, we introduce TFG-Flow, a novel training-free guidance method for multimodal generative flow. TFG-Flow addresses the curse-of-dimensionality while maintaining the property of unbiased sampling in guiding discrete variables. We validate TFG-Flow on four molecular design tasks and show that TFG-Flow has great potential in drug design by generating molecules with desired properties.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

Flow models are effective at progressively generating realistic images, but they generally struggle to capture long-range dependencies during the generation process as they compress all the information from previous time steps into a single corrupted image. To address this limitation, we propose integrating autoregressive modeling -- known for its excellence in modeling complex, high-dimensional joint probability distributions -- into flow models. During training, at each step, we construct causally-ordered sequences by sampling multiple images from the same semantic category and applying different levels of noise, where images with higher noise levels serve as causal predecessors to those with lower noise levels. This design enables the model to learn broader category-level variations while maintaining proper causal relationships in the flow process. During generation, the model autoregressively conditions the previously generated images from earlier denoising steps, forming a contextual and coherent generation trajectory. Additionally, we design a customized hybrid linear attention mechanism tailored to our modeling approach to enhance computational efficiency. Our approach, termed ARFlow, under 400k training steps, achieves 14.08 FID scores on ImageNet at 128 * 128 without classifier-free guidance, reaching 4.34 FID with classifier-free guidance 1.5, significantly outperforming the previous flow-based model SiT's 9.17 FID. Extensive ablation studies demonstrate the effectiveness of our modeling strategy and chunk-wise attention design.

Flow based generative models have charted an impressive path across multiple visual generation tasks by adhering to a simple principle: learning velocity representations of a linear interpolant. However, we observe that training velocity solely from the final layer output underutilizes the rich inter layer representations, potentially impeding model convergence. To address this limitation, we introduce DeepFlow, a novel framework that enhances velocity representation through inter layer communication. DeepFlow partitions transformer layers into balanced branches with deep supervision and inserts a lightweight Velocity Refiner with Acceleration (VeRA) block between adjacent branches, which aligns the intermediate velocity features within transformer blocks. Powered by the improved deep supervision via the internal velocity alignment, DeepFlow converges 8 times faster on ImageNet with equivalent performance and further reduces FID by 2.6 while halving training time compared to previous flow based models without a classifier free guidance. DeepFlow also outperforms baselines in text to image generation tasks, as evidenced by evaluations on MSCOCO and zero shot GenEval.

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

Recent AI-based 3D content creation has largely evolved along two paths: feed-forward image-to-3D reconstruction approaches and 3D generative models trained with 2D or 3D supervision. In this work, we show that existing feed-forward reconstruction methods can serve as effective latent encoders for training 3D generative models, thereby bridging these two paradigms. By reusing powerful pre-trained reconstruction models, we avoid computationally expensive encoder network training and obtain rich 3D latent features for generative modeling for free. However, the latent spaces of reconstruction models are not well-suited for generative modeling due to their unstructured nature. To enable flow-based model training on these latent features, we develop post-processing pipelines, including protocols to standardize the features and spatial weighting to concentrate on important regions. We further incorporate a 2D image space perceptual rendering loss to handle the high-dimensional latent spaces. Finally, we propose a multi-stream transformer-based rectified flow architecture to achieve linear scaling and high-quality text-conditioned 3D generation. Our framework leverages the advancements of feed-forward reconstruction models to enhance the scalability of 3D generative modeling, achieving both high computational efficiency and state-of-the-art performance in text-to-3D generation.

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Deep image inpainting has made impressive progress with recent advances in image generation and processing algorithms. We claim that the performance of inpainting algorithms can be better judged by the generated structures and textures. Structures refer to the generated object boundary or novel geometric structures within the hole, while texture refers to high-frequency details, especially man-made repeating patterns filled inside the structural regions. We believe that better structures are usually obtained from a coarse-to-fine GAN-based generator network while repeating patterns nowadays can be better modeled using state-of-the-art high-frequency fast fourier convolutional layers. In this paper, we propose a novel inpainting network combining the advantages of the two designs. Therefore, our model achieves a remarkable visual quality to match state-of-the-art performance in both structure generation and repeating texture synthesis using a single network. Extensive experiments demonstrate the effectiveness of the method, and our conclusions further highlight the two critical factors of image inpainting quality, structures, and textures, as the future design directions of inpainting networks.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.