# Ito maps for any-step SDEs

arXiv: https://arxiv.org/abs/2606.11156 · HTML: https://mlsanity.com/paper/2606.11156/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Meta Flow Maps enable scalable reward alignment](https://mlsanity.com/paper/2601.14430/) (2026)
- [Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling](https://mlsanity.com/paper/2510.24474/) (2025)

## Built on by (most cited first, 4 of 4)

- [Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners](https://mlsanity.com/paper/2606.29150/) (2026)
- [Twisted Schr"odinger Bridge Matching](https://mlsanity.com/paper/2607.16987/) (2026)
- [Interacting particle guidance for sampling reward-tilted generative priors](https://mlsanity.com/paper/2609.37227/) (2026)
- [Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps](https://mlsanity.com/paper/2610.09407/) (2026)

## Abstract (arXiv)

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 Ito map, an any-step stochastic flow map that takes an intermediate state and Brownian path and predicts future states in a single pass. The Ito map formulation yields novel estimators for inference-time control by providing cheap, differentiable access to posterior samples. Empirically, Ito 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.