Itô map enables any-step SDE integration for faster generative AI sampling

Recent one-step generative models like flow matching accelerate sampling by learning deterministic flow maps of underlying ODE dynamics. However, these methods leave open how to define an exact distillation procedure for stochastic dynamics (SDEs). Researchers from the paper 'Itô maps for any-step SDEs' address this gap by introducing the Itô map—a stochastic flow map that takes an intermediate state and a Brownian path as input and predicts future states in a single forward pass. This formulation yields novel estimators for inference-time control by providing cheap, differentiable access to posterior samples, enabling fine-grained steering of generated outputs.

Empirically, the method demonstrates strong results on both synthetic benchmarks and image-generation tasks. Itô maps produce diverse yet conditionally valid endpoint samples from fixed intermediate states, matching or exceeding the performance of traditional multi-step SDE solvers. The approach also supports strong steering performance, allowing users to control generated outputs at inference time without retraining. The paper establishes any-step SDE integration as a powerful primitive for posterior sampling and stochastic control, with potential applications in generative modeling, reinforcement learning, and scientific simulation. The work is available on arXiv (2606.11156) and includes code via the authors' repository.