aiqbench analysis
This research proposes a gradient-free sampling method for generative models by substituting standard score drift with high-frequency dithered cosine signals, effectively extending bounded extremum seeking to Itô processes. Theoretically, it converges to Langevin dynamics and reverse-time SDEs even for non-smooth energy landscapes, offering specific advantages in black-box latent-space scenarios where backpropagation is unavailable or targets shift over time. While not competitive with tuned gradient-based samplers for standard pixel-space tasks, the technique provides a robust alternative for tracking time-varying distributions in latent spaces without requiring explicit model gradients.
Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking
arXiv:2610.04568v1 Announce Type: cross Abstract: We introduce a sampling approach for energy- and score-based generative models that requires no gradient evaluations of the model. Replacing the drift term that would normally contain the score $\nabla_\mathbf{x} \log p_\theta(\bf{x})$ with a high-frequency dithered cosine of the model's \textit{value}, $\sqrt{\alpha\omega}\,\cos(\omega t + k \log p_\theta(\bf{x}))$, produces, in the high-frequency averaging limit, Langevin Markov chain Monte Carlo for energy-based models and the reverse-time SDE of score-based diffusion. We prove that trajectories of the dithered It\^{o} SDE converge to those of the target SDE, driven by the same Brownian motion, uniformly on compact time intervals in probability, by an averaging argument that extends bounded extremum seeking (ES) to It\^{o} processes, with an explicit $O(\omega^{-1/2})$ mean-square rate under global bounds. The approach is not confined to smooth targets: it extends to $C^{1,1}$ energies with discontinuous curvature (without ellipticity requirement) and to Sobolev energies whose Hessians exist only off measure zero sets; for Lipschitz energies with gradient kinks the averaged limit remains well posed; the Krylov-R\"ockner integrability class is the boundary of provability. The approach provides a hard \textit{a priori} bound on the per-step update rate and applies to explicitly time-varying targets on finite horizons. Gradient-free pixel-space sampling is not competitive with well-tuned backpropagation-based samplers at practical evaluation budgets; the regime where the approach offers an advantage is latent-space sampling when the model is a black box and the target drifts in time. We demonstrate latent-space tracking for time-varying images on CelebA-HQ ($256{\times}256$) from limited 1D projection measurements and latent-space EBM sampling on CIFAR-10.
Abstract:We introduce a sampling approach for energy- and score-based generative models that requires no gradient evaluations of the model. Replacing the drift term that would normally contain the score $\nabla_\mathbf{x} \log p_\theta(\bf{x})$ with a high-frequency dithered cosine of the model's \textit{value}, $\sqrt{\alpha\omega}\,\cos(\omega t + k \log p_\theta(\bf{x}))$, produces, in the high-frequency averaging limit, Langevin Markov chain Monte Carlo for energy-based models and the reverse-time SDE of score-based diffusion. We prove that trajectories of the dithered Itô SDE converge to those of the target SDE, driven by the same Brownian motion, uniformly on compact time intervals in probability, by an averaging argument that extends bounded extremum seeking (ES) to Itô processes, with an explicit $O(\omega^{-1/2})$ mean-square rate under global bounds. The approach is not confined to smooth targets: it extends to $C^{1,1}$ energies with discontinuous curvature (without ellipticity requirement) and to Sobolev energies whose Hessians exist only off measure zero sets; for Lipschitz energies with gradient kinks the averaged limit remains well posed; the Krylov-Röckner integrability class is the boundary of provability. The approach provides a hard \textit{a priori} bound on the per-step update rate and applies to explicitly time-varying targets on finite horizons. Gradient-free pixel-space sampling is not competitive with well-tuned backpropagation-based samplers at practical evaluation budgets; the regime where the approach offers an advantage is latent-space sampling when the model is a black box and the target drifts in time. We demonstrate latent-space tracking for time-varying images on CelebA-HQ ($256{\times}256$) from limited 1D projection measurements and latent-space EBM sampling on CIFAR-10.
Machine Learning (stat.ML); Machine Learning (cs.LG); Optimization and Control (math.OC); Computation (stat.CO)
arXiv:2610.04568 [stat.ML]
(or arXiv:2610.04568v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.04568 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 355 words
Related coverage
GEM Training: How Meta Doubled the Efficiency of Its LLM-Scale Ads Foundation Model
Meta Engineering · Aug 3, 2026
Scaling Reinforcement Learning for Diffusion Models via Velocity Matching
arXiv · Aug 26, 2026
WEIRDO: WEak resIdual Regularized DOob's h-transform diffusion alignment
arXiv · Oct 1, 2026
Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models
arXiv · Oct 8, 2026