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
191 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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Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
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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.
ASTRA reframes transition-state search as guided diffusion inference that samples the isodensity surface between metastable basins and converges to first-order saddles via score differences and physical forces.
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.
MindVLA-U1 introduces a unified streaming VLA with shared backbone, framewise memory, and language-guided action diffusion that surpasses human drivers on WOD-E2E planning metrics.
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.
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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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