Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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Score-Based Generative Modeling through Stochastic Differential Equations
186 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
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- abstract Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate
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A-CODE presents a fully atomic one-stage multimodal diffusion model for protein co-design that claims superior unconditional generation performance over prior one- and two-stage models plus a tenfold success-rate gain on hard binder-design tasks.
The García-Pintos feedback Hamiltonian equals the score function of the quantum trajectory distribution, linking quantum feedback to diffusion-model reversal.
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
OP-GRPO is the first off-policy GRPO method for flow-matching models that reuses trajectories via replay buffer and importance sampling corrections, matching on-policy performance with 34.2% of the training steps.
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
Flow-GRPO is the first online RL method for flow matching models, raising GenEval accuracy from 63% to 95% and text-rendering accuracy from 59% to 92% with little reward hacking.
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
Marginal-conditioned bridges enable training-free sampling from Flow Language Models by drawing clean one-hot endpoints from factorized posteriors and using Ornstein-Uhlenbeck bridges, preserving token marginals and reducing denoising error versus conditional-mean bridges.
HIR-ALIGN augments limited target data for hyperspectral restoration by creating proxy clean images, synthesizing aligned HSIs with blur-robust diffusion and warp-based transfer, then finetuning models to lower target-domain risk.
PGM replaces the intractable likelihood score in diffusion models with a closed-form Moreau score computed via proximal operators, enabling non-asymptotic sampling for inverse problems trained only on prior data.
Edit-Compass and EditReward-Compass are new unified benchmarks for fine-grained image editing evaluation and realistic reward modeling in reinforcement learning optimization.
TCE bridges domain gaps in offline RL by selectively using source data or generating target-aligned transitions via a dual score-based model, outperforming baselines in experiments.
AID amortizes guidance for diffusion inpainting by training a reusable module via an auxiliary Gaussian formulation and continuous-time actor-critic algorithm, improving quality-speed trade-off with under 1% overhead.
Flow map policies enable fast one-step inference for flow-based RL policies, and FMQ provides an optimal closed-form Q-guided target for offline-to-online adaptation under trust-region constraints, achieving SOTA performance.
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.
Muninn accelerates diffusion trajectory planners up to 4.6x by spending an uncertainty budget to decide when to cache denoiser outputs, preserving performance and certifying bounded deviation from full computation.
ΔLPS is a gradient-guided discrete posterior sampler for inverse problems that works with masked or uniform discrete diffusion priors and outperforms prior discrete methods on image restoration tasks.
MixtureTT performs direct per-stem timbre transfer on polyphonic mixtures via a shared diffusion transformer, outperforming single-stem baselines on SATB choral data while eliminating cascaded separation errors.
Wasserstein Lagrangian Mechanics learns second-order population dynamics from observed marginals without specifying the Lagrangian and outperforms gradient flow methods on periodic dynamics like vortex motion and flocking.
A training-free adaptive subspace projection method mitigates semantic collapsing in generative personalization by isolating and adjusting drift in a low-dimensional subspace using the stable pre-trained embedding as anchor.
K-DSM uses per-feature kurtosis to set noise scales in DSM, enabling effective single-scale anomaly detection on tabular benchmarks in both semi-supervised and unsupervised settings.
Path-Coupled Bellman Flows use source-consistent Bellman-coupled paths and a lambda-parameterized control-variate to learn return distributions via flow matching, improving fidelity and stability over prior DRL approaches.
citing papers explorer
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Generative Modeling with Flux Matching
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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A-CODE: Fully Atomic Protein Co-Design with Unified Multimodal Diffusion
A-CODE presents a fully atomic one-stage multimodal diffusion model for protein co-design that claims superior unconditional generation performance over prior one- and two-stage models plus a tenfold success-rate gain on hard binder-design tasks.
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The Feedback Hamiltonian is the Score Function: A Diffusion-Model Framework for Quantum Trajectory Reversal
The García-Pintos feedback Hamiltonian equals the score function of the quantum trajectory distribution, linking quantum feedback to diffusion-model reversal.
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Query Lower Bounds for Diffusion Sampling
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
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OP-GRPO: Efficient Off-Policy GRPO for Flow-Matching Models
OP-GRPO is the first off-policy GRPO method for flow-matching models that reuses trajectories via replay buffer and importance sampling corrections, matching on-policy performance with 34.2% of the training steps.
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Generative models on phase space
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
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Flow-GRPO: Training Flow Matching Models via Online RL
Flow-GRPO is the first online RL method for flow matching models, raising GenEval accuracy from 63% to 95% and text-rendering accuracy from 59% to 92% with little reward hacking.
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Large Language Diffusion Models
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
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Sampling from Flow Language Models via Marginal-Conditioned Bridges
Marginal-conditioned bridges enable training-free sampling from Flow Language Models by drawing clean one-hot endpoints from factorized posteriors and using Ornstein-Uhlenbeck bridges, preserving token marginals and reducing denoising error versus conditional-mean bridges.
-
HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation
HIR-ALIGN augments limited target data for hyperspectral restoration by creating proxy clean images, synthesizing aligned HSIs with blur-robust diffusion and warp-based transfer, then finetuning models to lower target-domain risk.
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Proximal-Based Generative Modeling for Bayesian Inverse Problems
PGM replaces the intractable likelihood score in diffusion models with a closed-form Moreau score computed via proximal operators, enabling non-asymptotic sampling for inverse problems trained only on prior data.
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Edit-Compass & EditReward-Compass: A Unified Benchmark for Image Editing and Reward Modeling
Edit-Compass and EditReward-Compass are new unified benchmarks for fine-grained image editing evaluation and realistic reward modeling in reinforcement learning optimization.
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Bridging Domain Gaps with Target-Aligned Generation for Offline Reinforcement Learning
TCE bridges domain gaps in offline RL by selectively using source data or generating target-aligned transitions via a dual score-based model, outperforming baselines in experiments.
-
Amortized Guidance for Image Inpainting with Pretrained Diffusion Models
AID amortizes guidance for diffusion inpainting by training a reusable module via an auxiliary Gaussian formulation and continuous-time actor-critic algorithm, improving quality-speed trade-off with under 1% overhead.
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Aligning Flow Map Policies with Optimal Q-Guidance
Flow map policies enable fast one-step inference for flow-based RL policies, and FMQ provides an optimal closed-form Q-guided target for offline-to-online adaptation under trust-region constraints, achieving SOTA performance.
-
One-Step Generative Modeling via Wasserstein Gradient Flows
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
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On the Approximation Complexity of Matrix Product Operator Born Machines
MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.
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Muninn: Your Trajectory Diffusion Model But Faster
Muninn accelerates diffusion trajectory planners up to 4.6x by spending an uncertainty budget to decide when to cache denoiser outputs, preserving performance and certifying bounded deviation from full computation.
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Discrete Langevin-Inspired Posterior Sampling
ΔLPS is a gradient-guided discrete posterior sampler for inverse problems that works with masked or uniform discrete diffusion priors and outperforms prior discrete methods on image restoration tasks.
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Remix the Timbre: Diffusion-Based Style Transfer Across Polyphonic Stems
MixtureTT performs direct per-stem timbre transfer on polyphonic mixtures via a shared diffusion transformer, outperforming single-stem baselines on SATB choral data while eliminating cascaded separation errors.
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A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
Wasserstein Lagrangian Mechanics learns second-order population dynamics from observed marginals without specifying the Lagrangian and outperforms gradient flow methods on periodic dynamics like vortex motion and flocking.
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Adaptive Subspace Projection for Generative Personalization
A training-free adaptive subspace projection method mitigates semantic collapsing in generative personalization by isolating and adjusting drift in a low-dimensional subspace using the stable pre-trained embedding as anchor.
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Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection
K-DSM uses per-feature kurtosis to set noise scales in DSM, enabling effective single-scale anomaly detection on tabular benchmarks in both semi-supervised and unsupervised settings.
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Path-Coupled Bellman Flows for Distributional Reinforcement Learning
Path-Coupled Bellman Flows use source-consistent Bellman-coupled paths and a lambda-parameterized control-variate to learn return distributions via flow matching, improving fidelity and stability over prior DRL approaches.
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Arena as Offline Reward: Efficient Fine-Grained Preference Optimization for Diffusion Models
ArenaPO infers Gaussian capability distributions from pairwise preferences and applies truncated-normal latent inference to derive fine-grained offline rewards for preference optimization of text-to-image diffusion models.
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DBMSolver: A Training-free Diffusion Bridge Sampler for High-Quality Image-to-Image Translation
DBMSolver is a new training-free sampler using exponential integrators that reduces NFEs by up to 5x and improves quality in diffusion bridge model-based image-to-image translation tasks.
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Beyond Penalization: Diffusion-based Out-of-Distribution Detection and Selective Regularization in Offline Reinforcement Learning
DOSER detects OOD actions via diffusion-model denoising error and applies selective regularization based on predicted transitions, proving gamma-contraction with performance bounds and outperforming priors on offline RL benchmarks.
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Tempered Guided Diffusion
Tempered Guided Diffusion uses annealed SMC to produce consistent particle approximations to the posterior for training-free conditional diffusion sampling, outperforming independent guided trajectories in experiments.
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PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics
PerFlow embeds physics constraints into rectified flow sampling through guidance-free conditioning and constraint-preserving projections, achieving efficient sparse reconstruction and uncertainty quantification for spatiotemporal dynamics.
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PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution
PODiff performs conditional diffusion in a fixed, variance-ordered POD latent space to enable efficient probabilistic super-resolution of high-dimensional scientific fields with lower memory and better-calibrated uncertainty than pixel-space or dropout baselines.
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Inferring Active Neural Circuits Using Diffusion Scores
SBTG recovers the Jacobian of the nonlinear transition map between brain states by multiplying cross-block scores from denoising models, enabling inference of lag-specific directed interactions in neural population data such as C. elegans calcium imaging.
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Generative Modeling with Orbit-Space Particle Flow Matching
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
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Towards Efficient and Expressive Offline RL via Flow-Anchored Noise-conditioned Q-Learning
FAN achieves state-of-the-art offline RL performance on robotic tasks by anchoring flow policies and using single-sample noise-conditioned Q-learning, with proven convergence and reduced runtimes.
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Decentralized Proximal Stochastic Gradient Langevin Dynamics
DE-PSGLD is the first decentralized MCMC sampler for constrained convex domains that converges to a regularized Gibbs distribution with explicit 2-Wasserstein bounds for agents and network averages.
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GD4: Graph-based Discrete Denoising Diffusion for MIMO Detection
GD4 is a graph-based discrete denoising diffusion method for MIMO detection that yields higher-quality suboptimal solutions than prior diffusion detectors and classical baselines under similar compute budgets in both under- and over-determined settings.
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ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space
ABC enables any-subset autoregressive generation of continuous stochastic processes via non-Markovian diffusion bridges that track physical time and allow path-dependent conditioning.
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How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG is a training-free, single-trajectory guidance method for flow models derived from optimal control that achieves strong reward alignment with only 3 NFEs.
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Oracle Noise: Faster Semantic Spherical Alignment for Interpretable Latent Optimization
Oracle Noise optimizes diffusion model noise on a Riemannian hypersphere guided by key prompt words to preserve the Gaussian prior, eliminate norm inflation, and achieve faster semantic alignment than Euclidean methods.
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$Z^2$-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models
Z²-Sampling implicitly realizes zero-cost zigzag trajectories for curvature-aware semantic alignment in diffusion models by reducing multi-step paths via operator dualities and temporal caching while synthesizing a directional derivative penalty.
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Dream-Cubed: Controllable Generative Modeling in Minecraft by Training on Billions of Cubes
Dream-Cubed releases a billion-scale voxel dataset and 3D diffusion models that generate controllable Minecraft worlds by operating directly on blocks.
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Frequency-Forcing: From Scaling-as-Time to Soft Frequency Guidance
Frequency-Forcing guides pixel flow-matching with a data-derived low-frequency auxiliary stream to softly enforce scale-ordered generation, improving FID on ImageNet-256 over baselines.
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HP-Edit: A Human-Preference Post-Training Framework for Image Editing
HP-Edit introduces a post-training framework and RealPref-50K dataset that uses a VLM-based HP-Scorer to align diffusion image editing models with human preferences, improving outputs on Qwen-Image-Edit-2509.
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Learning to Credit the Right Steps: Objective-aware Process Optimization for Visual Generation
OTCA improves GRPO training for visual generation by estimating step importance in trajectories and adaptively weighting multiple reward objectives.
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Generative Texture Filtering
A two-stage fine-tuning strategy on pre-trained generative models enables effective texture filtering that outperforms prior methods on challenging cases.
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Guiding Distribution Matching Distillation with Gradient-Based Reinforcement Learning
GDMD replaces raw-sample rewards with distillation-gradient rewards in RL-guided diffusion distillation, yielding 4-step models that surpass their multi-step teachers on GenEval and human preference metrics.
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NI Sampling: Accelerating Discrete Diffusion Sampling by Token Order Optimization
NI Sampling accelerates discrete diffusion language models up to 14.3 times by training a neural indicator to select which tokens to sample at each step using a trajectory-preserving objective.
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Long-Text-to-Image Generation via Compositional Prompt Decomposition
PRISM lets pre-trained text-to-image models handle long prompts by breaking them into compositional parts, predicting noise separately, and merging outputs via energy-based conjunction, matching fine-tuned models while generalizing better to prompts over 500 tokens.
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Latent Fourier Transform
LatentFT uses latent-space Fourier transforms and frequency masking in diffusion autoencoders to enable timescale-specific manipulation of musical structure in generative models.
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Structure-Adaptive Sparse Diffusion in Voxel Space for 3D Medical Image Enhancement
A sparse voxel-space diffusion method with structure-adaptive modulation achieves up to 10x training speedup and state-of-the-art results for 3D medical image denoising and super-resolution.
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Grokking of Diffusion Models: Case Study on Modular Addition
Diffusion models show grokking on modular addition by composing periodic operand representations in simple data regimes or by separating arithmetic computation from visual denoising across timesteps in varied regimes.