ManifoldCache: Training-Free Diffusion Acceleration via Constraint Manifold Caching

2026-10-03

AI Summary

This study addresses the prohibitively slow inference of scientific diffusion models imposed by geometric constraints, noting that existing acceleration methods often violate these constraints or induce mode confusion. To overcome this, the work proposes the first training-free accelerator tailored for constrained manifold diffusion models. By leveraging the orthogonal decomposition property of conditional scores, it is theoretically proven that the midpoint of the noise schedule constitutes a safe caching boundary, within which tangential components are cached to enable larger sampling steps. This approach requires neither additional training nor calibration data. It significantly accelerates the generative process while strictly preserving physicochemical constraint fidelity, thereby achieving efficient zero-overhead sampling.

Abstract

Diffusion models for structured scientific generation must produce samples satisfying hard geometric constraints imposed by physics, chemistry, or biology, yet inference in these settings is prohibitively slow, demanding hundreds to thousands of neural-function evaluations per sample. We unify eight state-of-the-art models spanning medical volumetrics, molecular conformations, protein backbone design, crystal structure prediction, and multi-view 3D scenes under a single abstraction, Constraint-Manifold Diffusion Models (CMDMs), in which the target distribution is supported on a manifold defined by an externally specified constraint map. All existing acceleration families fail on this class: quantization exhausts memory on high-dimensional volumetric operators; pruning breaks constraint fidelity; fast ODE solvers allow trajectories to drift off the constraint manifold; and feature-caching heuristics are blind to constraint geometry, inducing mode confusion in the high-noise regime. We introduce ManifoldCache, the first training-free, data-free accelerator designed from first principles for CMDMs. The key insight is that the conditional score decomposes orthogonally into a normal component, which enforces constraint satisfaction, and a tangential component, which navigates within the manifold. Exploiting this structure, we prove that the noise-schedule midpoint is a sharp safe-caching boundary: caching before it incurs provably bounded error, while caching after it guarantees a strictly positive fraction of trajectories suffer mode confusion, a gap that persists up to the boundary. We further prove that deeper network blocks admit provably larger certified cache strides within the safe phase, as a consequence of the score decomposition propagating through block Jacobians. The resulting schedule requires no calibration data, along with zero training overhead.

Problem

• Diffusion Models
• Inference Acceleration
• Constraint Manifold
• Scientific Generation
• Training-Free

Innovation

• Constraint-Manifold Diffusion Models
• Training-Free Acceleration
• Score Decomposition
• Safe-Caching Boundary
• ManifoldCache