Graduate Student / Postdoc Seminar

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Constrained Deep Generative Modeling via Augmented Lagrangian Langevin Dynamics

Speaker: Matthieu Blanke, Courant Institute, New York University

Location: Warren Weaver Hall 1302

Date: Friday, October 3, 2025, 1 p.m.

Synopsis:

Generative deep learning methods have become powerful tools for modeling complex data distributions. While they produce perceptually convincing samples in imaging tasks, many scientific applications in climate sciences require outputs to satisfy strict mathematical constraints, such as conservation laws or dynamical equations. Enforcing such constraints at sampling time, especially in a zero-shot setting without retraining, is therefore critical for physically consistent predictions. In this talk, we present a mathematical framework for constrained sampling based on the variational formulation of Langevin dynamics, and duality in Wasserstein space. Building on this foundation, we introduce Split Augmented Lagrangian Langevin, a novel primal-dual sampling algorithm that progressively enforces constraints via variable splitting, with convergence guarantees. We demonstrate its effectiveness on physically constrained generative modeling tasks. Applications include energy-conserving diffusion models for data assimilation and inverse problems, and dynamics-constrained generative priors for non-convex optimal control problems.

Joint work with Yongquan Qu, Sara Shamekh and Pierre Gentine:
https://arxiv.org/abs/2505.18017