Abstract: Diffusion-based trajectory planners can synthesize rich, multimodal robot motions from demonstrations, 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 already 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 spanning offline RL planning (D4RL), configuration-space motion planning, and visuomotor diffusion policies, Muninn delivers up to 4.6× wall-clock speedups across several trajectory diffusion planners and diffusion policies by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies—at a user-chosen deviation tolerance and risk level—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.