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.
Theoretical guarantees for sampling and inference in generative models with latent diffusions
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abstract
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion. We make the following contributions: We provide a unified viewpoint on both sampling and variational inference in such generative models through the lens of stochastic control. We quantify the expressiveness of diffusion-based generative models. Specifically, we show that one can efficiently sample from a wide class of terminal target distributions by choosing the drift of the latent diffusion from the class of multilayer feedforward neural nets, with the accuracy of sampling measured by the Kullback-Leibler divergence to the target distribution. Finally, we present and analyze a scheme for unbiased simulation of generative models with latent diffusions and provide bounds on the variance of the resulting estimators. This scheme can be implemented as a deep generative model with a random number of layers.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
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Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents
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.
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Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control
Adjoint matching objectives derived from the Stochastic Maximum Principle have critical points satisfying HJB stationarity conditions for SOC problems with control-dependent drift and diffusion.
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MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data
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