PPR: new sampler constrains diffusion models in physics

An algorithm called Predict-Project-Renoise (PPR) forces diffusion-model samples to satisfy hard constraints without retraining the underlying model, its authors say. In a preprint on arXiv, Omer Rochman-Sharabi and Gilles Louppe argue that 'diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency.'

The method works by 'iteratively projecting through the denoiser and renoising via the forward kernel.' It is tested on 2D distributions, the Kuramoto-Sivashinsky equation, and a global weather forecasting problem the authors describe as having 10^8 dimensions. All three components are essential, they argue: denoiser projection keeps outputs on the data manifold, while renoising and iteration steer samples toward the constrained distribution. On that combination, the paper reports PPR achieving 'simultaneously low constraint violations and high distributional accuracy.'

The preprint was first submitted on January 28, 2026, with v2 revised May 13, 2026. Two of the researchers we follow had already posted the link by the time of writing.