Uncertainty-Aware Sequential Monte Carlo for Hard-Constrained Diffusion

Deploying diffusion models often requires strict constraints, yet existing methods have distinct drawbacks: projection-based approaches rely on restrictive assumptions and can distort the constrained distribution, while particle methods construct intermediate potentials from point predictions of the terminal state, ignoring posterior uncertainty. Moreover, many practical constraints are non-differentiable or black-box, so gradients are unavailable. We introduce Uncertainty-Aware Sequential Monte Carlo (UA-SMC), a projection-free sampler for hard-constrained diffusion. UA-SMC directly approximates the probability of eventual constraint satisfaction and uses it as a Feynman–Kac potential. A practical time-dependent schedule captures contracting terminal uncertainty while avoiding state-dependent gradients. We analyze how approximation error in these potentials propagates to the intermediate targets and derive a finite-particle error bound. Across porous material design, rare-event sampling for nonlinear dynamics, and copyright-safe text-to-image generation, UA-SMC consistently attains high constraint satisfaction and distributional fidelity for non-differentiable and black-box constraints.