A Fixed-Point Algorithm for Constraining Pre-trained Diffusion Models

Three-dimensional diffusion models have emerged as a powerful tool to extract priors from large geometric datasets. However, exploiting these priors in generative high-precision applications (e.g., the design of medical prosthetics) requires a strategy for enforcing hard constraints on each generated shape. Unfortunately, we find that existing algorithms to impose these constraints on pre-trained diffusion models are inadequate for a large class of 3D generative tasks, as they either modify the denoised generation, risking escaping the data distribution, or rely on guiding the noisy reverse diffusion trajectory, very often failing to satisfy the constraints exactly. We introduce a fixed-point strategy for modifying the reverse diffusion trajectory without escaping the data distribution, improving the tradeoff between plausibility and feasibility of the generations. We showcase our method's performance on the 3D generative tasks that motivate its design, on which it outperforms every considered baseline, as well as on common 2D and multi-dimensional benchmarks.