Itô maps for any-step SDEs
Abstract
Recent one-step generative models accelerate sampling by learning deterministic flow maps of the underlying dynamics. These methods rely on learning from ordinary differential equations, leaving open how to define an exact distillation procedure for stochastic dynamics. We introduce the Itô map, an any-step stochastic flow map that takes an intermediate state and Brownian path and predicts future states in a single pass. The Itô map formulation yields novel estimators for inference-time control by providing cheap, differentiable access to posterior samples. Empirically, Itô maps produce diverse, conditionally valid endpoint samples from fixed intermediate states and support strong steering performance on synthetic and image-generation benchmarks. These results establish any-step SDE integration as a useful primitive for posterior sampling and stochastic control.
Related
- Posterior sampling by source-space MCMC via prior-based few-step transport maps
- Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps
- A criterion of density for solutions of Poisson-driven SDEs
- Small time asymptotics for kinetic SDEs with singular drift
- A stable limit theorem for SDEs driven by multiplicative α-stable processes
BibTeX
@misc{pan2026itô,
title = {{Itô maps for any-step SDEs}},
author = {Zhengkai Pan and Peter Potaptchik and Wenxi Yao and Michael S. Albergo and Jakiw Pidstrigach},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.11156},
eprint = {2606.11156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.11156},
}
RIS
TY - UNPB
TI - Itô maps for any-step SDEs
AU - Zhengkai Pan
AU - Peter Potaptchik
AU - Wenxi Yao
AU - Michael S. Albergo
AU - Jakiw Pidstrigach
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2606.11156
UR - https://arxiv.org/abs/2606.11156
AB - Recent one-step generative models accelerate sampling by learning deterministic flow maps of the underlying dynamics. These methods rely on learning from ordinary differential equations, leaving open how to define an exact distillation procedure for stochastic dynamics. We introduce the Itô map, an any-step stochastic flow map that takes an intermediate state and Brownian path and predicts future states in a single pass. The Itô map formulation yields novel estimators for inference-time control by providing cheap, differentiable access to posterior samples. Empirically, Itô maps produce diverse, conditionally valid endpoint samples from fixed intermediate states and support strong steering performance on synthetic and image-generation benchmarks. These results establish any-step SDE integration as a useful primitive for posterior sampling and stochastic control.
ER -