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
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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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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.
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.
MF-PID turns independent diffusion samples into mean-field interacting agents, proving that quadratic interactions yield exact linear mean interpolation and delivering 19-24% energy savings in demand-response control.
Föllmer processes are variationally optimal among generative diffusions because they minimize the impact of drift estimation error on path-space KL divergence, rendering different interpolation schedules statistically equivalent.
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.
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
A control-theoretic linear program yields value-driven transport policies for generative modeling with straight paths and simulation-free training.
JET is a conditional flow matching framework that generates EEG as continuous raw sequences with added constraints for spectral and temporal properties, achieving over 40% lower TS-FID than prior discrete denoising methods on three benchmarks.
Linear-DPO replaces sigmoid utility with linear utility and adds EMA reference to improve preference alignment in diffusion and flow-matching text-to-image models.
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