Deep generative models, AI systems that can learn to create realistic data, are increasingly used to represent complex physical systems. However, these models often produce results that break basic physical laws, such as conservation of energy or mass. This LEAP study , led by Matthieu Blanke, introduces a new method, called Split Augmented Langevin (SAL), that ensures AI-generated outputs obey these fundamental constraints. By enforcing physical constraints in the sampling algorithm of pre-trained diffusion models, the approach makes AI-based simulations and forecasts more accurate and reliable. The method shows promising results in climate science applications, paving the way for AI tools that better respect the laws of nature.