# Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants

arXiv: https://arxiv.org/abs/2504.05852 · HTML: https://mlsanity.com/paper/2504.05852/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2025.

## Built on by (most cited first, 9 of 9)

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- [Divergence-Free Diffusion Models for Incompressible Fluid Flows](https://mlsanity.com/paper/2601.19368/) (2026)
- [Variational Optimality of F"ollmer Processes in Generative Diffusions](https://mlsanity.com/paper/2602.10989/) (2026)
- [LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics](https://mlsanity.com/paper/2603.28324/) (2026)
- [A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants](https://mlsanity.com/paper/2610.03396/) (2026)
- [Xaurora: Generative Weather Forecasting with Denoising Stochastic Interpolants from a Foundation Model Prior](https://mlsanity.com/paper/2610.06509/) (2026)

## Abstract (arXiv)

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.