Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach

The paper introduces a conditional diffusion guidance framework that enforces hard constraints in generated samples, ensuring compliance with specified events with probability one. It employs Doob's h-transform and martingale processes to create a drift correction without altering the pretrained score network, along with two novel off-policy learning algorithms for estimating the necessary gradients. This work is significant for practitioners in safety-critical applications, as it provides a robust method for generating samples that meet strict constraints, thus enhancing reliability in rare-event simulations.