Researchers Introduce Itô Maps for Improved Stochastic Differential Equation Sampling
Researchers have proposed the Itô map, a stochastic flow map capable of predicting future states of a stochastic dynamical system in a single forward pass given an intermediate state and Brownian path. Unlike existing one-step generative models that rely on ordinary differential equations, the Itô map extends distillation to stochastic differential equations (SDEs) of arbitrary step size. The method offers practical benefits for posterior sampling and stochastic control in machine learning applications, including image generation.
A preprint posted to arXiv introduces the Itô map, a framework designed to accelerate sampling from stochastic differential equations by learning a deterministic mapping over any number of integration steps. Prior one-step generative models have achieved fast sampling by distilling ordinary differential equation trajectories, but no analogous exact procedure existed for stochastic dynamics — a gap this work aims to close. The Itô map takes an intermediate state and a Brownian path as inputs and predicts future states in a single neural network pass, enabling cheap and differentiable access to posterior samples. This differentiability is leveraged to derive novel estimators for inference-time control, allowing the model to be steered toward desired outcomes without retraining. Empirical evaluations on synthetic tasks and image-generation benchmarks demonstrate that Itô maps produce diverse, conditionally valid samples and exhibit strong steering performance. The authors argue that any-step SDE integration, as formalized here, constitutes a broadly useful primitive for both posterior sampling and stochastic control in generative modeling.
What's missing
The preprint has not yet undergone peer review.
What different sources said
- arXiv cs.LGCenter
It\^o maps for any-step SDEs
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