# ManifoldCache: Training-Free Diffusion Acceleration via Constraint Manifold Caching

arXiv: https://arxiv.org/abs/2610.04510 · HTML: https://mlsanity.com/paper/2610.04510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 43 of its 48 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [Structural Pruning for Diffusion Models](https://mlsanity.com/paper/2305.10924/) (2023)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [Accelerating Diffusion Transformers with Token-wise Feature Caching](https://mlsanity.com/paper/2410.05317/) (2024)
- [Real-Time Video Generation with Pyramid Attention Broadcast](https://mlsanity.com/paper/2408.12588/) (2024)
- [dKV-Cache: The Cache for Diffusion Language Models](https://mlsanity.com/paper/2505.15781/) (2025)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [FORA: Fast-Forward Caching in Diffusion Transformer Acceleration](https://mlsanity.com/paper/2407.01425/) (2024)
- [From Reusing to Forecasting: Accelerating Diffusion Models with TaylorSeers](https://mlsanity.com/paper/2503.06923/) (2025)
- [FasterCache: Training-Free Video Diffusion Model Acceleration with High Quality](https://mlsanity.com/paper/2410.19355/) (2024)
- [Adaptive Caching for Faster Video Generation with Diffusion Transformers](https://mlsanity.com/paper/2411.02397/) (2024)
- [Conditional Diffusion Models for Semantic 3D Brain MRI Synthesis](https://mlsanity.com/paper/2305.18453/) (2023)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [TFMQ-DM: Temporal Feature Maintenance Quantization for Diffusion Models](https://mlsanity.com/paper/2311.16503/) (2023)
- [Proteina: Scaling Flow-based Protein Structure Generative Models](https://mlsanity.com/paper/2503.00710/) (2025)
- [Learning Mixtures of Gaussians Using the DDPM Objective](https://mlsanity.com/paper/2307.01178/) (2023)
- [QuEST: Low-bit Diffusion Model Quantization via Efficient Selective Finetuning](https://mlsanity.com/paper/2402.03666/) (2024)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)
- [SV4D 2.0: Enhancing Spatio-Temporal Consistency in Multi-View Video Diffusion for High-Quality 4D Generation](https://mlsanity.com/paper/2503.16396/) (2025)

## Abstract (arXiv)

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.