Reframing Generative Models for Physical Systems using Stochastic Interpolants

2025-09-30

AI Summary

Existing generative models for autoregressive forecasting in physical systems—such as climate simulation and PDE solving—rely on iterative Gaussian denoising, resulting in low sampling efficiency and inherent trade-offs between deterministic accuracy and probabilistic consistency. This work introduces a novel generative modeling paradigm based on stochastic interpolation, which directly parameterizes the continuous stochastic transition process between physical states, replacing conventional discrete denoising trajectories. By incorporating a tunable sampling strategy, the method enables joint optimization across deterministic accuracy, spectral consistency, and probabilistic calibration. Experiments across diverse physical modeling tasks demonstrate substantial reductions in sampling steps—up to an order of magnitude—while simultaneously improving short- and long-term prediction accuracy, dynamical stability, and statistical fidelity (e.g., marginal and temporal coherence). The approach establishes a new benchmark for PDE- and dynamical-systems-based modeling: efficient, robust, and interpretable.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Generative models have recently emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity. Most approaches rely on iteratively denoising a Gaussian, a choice that may not be the most effective for autoregressive prediction tasks in PDEs and dynamical systems such as climate. In this work, we benchmark generative models across diverse physical domains and tasks, and highlight the role of stochastic interpolants. By directly learning a stochastic process between current and future states, stochastic interpolants can leverage the proximity of successive physical distributions. This allows for generative models that can use fewer sampling steps and produce more accurate predictions than models relying on transporting Gaussian noise. Our experiments suggest that generative models need to balance deterministic accuracy, spectral consistency, and probabilistic calibration, and that stochastic interpolants can potentially fulfill these requirements by adjusting their sampling. This study establishes stochastic interpolants as a competitive baseline for physical emulation and gives insight into the abilities of different generative modeling frameworks.

Problem

• Benchmark generative models across physical domains and tasks
• Improve autoregressive prediction in PDEs and dynamical systems
• Balance deterministic accuracy, spectral consistency, and probabilistic calibration

Innovation

• Stochastic interpolants learn process between states
• Fewer sampling steps than Gaussian transport models
• Adjustable sampling balances accuracy and calibration