Learning Pareto Manifolds for Diffusion Models

We propose Pareto-front Guided Diffusion (PGDiff), a novel diffusion framework that improves the learning of the reverse process by enforcing three categories of constraints, including initial/boundary constraints, governing constraints and inequality constraints. Unlike existing methods that applies constraints post-hoc or via penalty terms, PGDiff introduces a step-wise optimization architecture that inserts the intermediate state optimized by the Multiple Gradient Descent Algorithm between denoising steps. This enables the generated samples to move toward the Pareto front in the objective space, allowing progressive satisfaction of multiple complex constraints while preserving sample fidelity. Experiments on the path planning tasks and the PDEs solvers show PGDiff achieves a high constraint satisfaction under multi-constraints settings, outperforming several state-of-the-art baselines.