发表机构
Indian Institute of Technology, Delhi; Indian School of Mines, Dhanbad（德里印度理工学院; 丹巴德印度矿业学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
ManifoldCache利用条件分数在约束流形上的正交分解，在噪声调度中点前缓存以零训练开销加速CMDMs推理，并证明边界前误差有界、边界后存在模式混淆风险。
AI 中文摘要
用于结构化科学生成的扩散模型必须产生满足物理、化学或生物学所施加的硬几何约束的样本，然而这些设置中的推理速度极慢，每个样本需要数百到数千次神经函数评估。我们将涵盖医学体积成像、分子构象、蛋白质骨架设计、晶体结构预测和多视图3D场景的八种最先进模型统一到一个抽象框架下，即约束流形扩散模型（CMDMs），其中目标分布由外部指定的约束映射所定义的流形支撑。所有现有的加速族在此类模型上均告失败：量化在高维体积算子上耗尽内存；剪枝破坏约束保真度；快速ODE求解器允许轨迹偏离约束流形；而特征缓存启发式方法对约束几何不敏感，在高噪声区域引起模式混淆。我们引入了ManifoldCache，这是首个为CMDMs从第一性原理设计的免训练、免数据加速器。关键洞察在于条件分数正交分解为一个法向分量（负责强制满足约束）和一个切向分量（负责在流形内导航）。利用这一结构，我们证明了噪声调度中点是一个尖锐的安全缓存边界：在它之前缓存会产生可证明有界的误差，而在它之后缓存则保证严格正比例的轨迹遭受模式混淆，这一差距一直持续到边界。我们进一步证明，在安全阶段内，更深的网络块可允许可证明更大的认证缓存步长，这是分数分解通过块雅可比矩阵传播的结果。由此产生的调度无需校准数据，且零训练开销。
英文摘要
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.
