# Muninn: Your Trajectory Diffusion Model But Faster

arXiv: https://arxiv.org/abs/2605.09999 · HTML: https://mlsanity.com/paper/2605.09999/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 58 of its 74 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 58)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [Diffusion-based Generation, Optimization, and Planning in 3D Scenes](https://mlsanity.com/paper/2301.06015/) (2023)
- [FastBERT: a Self-distilling BERT with Adaptive Inference Time](https://mlsanity.com/paper/2004.02178/) (2020)
- [Token Merging for Fast Stable Diffusion](https://mlsanity.com/paper/2303.17604/) (2023)
- [Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation](https://mlsanity.com/paper/2405.07503/) (2024)

## Abstract (arXiv)

Diffusion-based trajectory planners can synthesize rich, multimodal robot motions, but their iterative denoising makes online planning and control prohibitively slow. Existing accelerations either modify the sampler or compress the network--sacrificing plan quality or requiring retraining without accounting for downstream control risk. We address the problem of making diffusion-based trajectory planners fast enough for real-time robot use without retraining the model or sacrificing trajectory quality, and in a way that works across diverse state-space diffusion architectures. Our key insight is that diffusion trajectory planners expose two signals we can exploit: a cheap probe of how their internal trajectory representation changes across steps, and analytic coefficients that describe how denoiser errors affect the sampler's state update. By calibrating the first signal against the second on offline runs, we obtain a per-step score that upper-bounds how far the final trajectory can deviate when we reuse a cached denoiser output, and we treat this bound as an uncertainty budget that we can spend over the denoising process. Building on this insight, we present Muninn, a training-free caching wrapper that tracks this uncertainty budget during sampling and, at each diffusion step, chooses between reusing a cached denoiser output when the predicted deviation is small and recomputing the denoiser when it is not. Across standard benchmarks Muninn delivers up to 4.6x wall-clock speedups across several trajectory diffusion models by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies that cached rollouts remain within a specified distance of their full-compute counterparts, and we validate these gains in real-time closed-loop navigation and manipulation hardware deployments. Project page: https://github.com/gokulp01/Muninn.