# GRACE: Gradient-Free Robot Action Generation via Combined Diffusion-MPPI Posterior Mean Estimation

arXiv: https://arxiv.org/abs/2607.21661 · HTML: https://mlsanity.com/paper/2607.21661/

## 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 15 of its 23 references that are in the map.
- First posted on arXiv 22 Jul 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, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)
- [DynaGuide: Steering Diffusion Polices with Active Dynamic Guidance](https://mlsanity.com/paper/2506.13922/) (2025)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Inference-Time Policy Steering through Human Interactions](https://mlsanity.com/paper/2411.16627/) (2024)
- [Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing](https://mlsanity.com/paper/2409.15610/) (2024)
- [Multimodal Trajectory Optimization for Motion Planning](https://mlsanity.com/paper/2003.07054/) (2020)
- [Joint Model-based Model-free Diffusion for Planning with Constraints](https://mlsanity.com/paper/2509.08775/) (2025)
- [Unifying Model Predictive Path Integral Control, Reinforcement Learning, and Diffusion Models for Optimal Control and Planning](https://mlsanity.com/paper/2502.20476/) (2025)

## Abstract (arXiv)

Diffusion policies generate multimodal robot action sequences from demonstrations, but steering them toward deployment-time constraints typically relies on differentiable guidance costs. This excludes many practical safety constraints, such as binary collision checks, joint limits, and black-box rollout costs that are nondifferentiable. We propose Gradient-free Robot Action generation via Combined diffusion-MPPI posterior mean Estimation (GRACE), which guides a pretrained diffusion policy with Model Predictive Path Integral (MPPI) control using only forward cost evaluations. Building on the common score-ascent structure of diffusion and MPPI, GRACE constructs a cost-conditioned guidance posterior at each reverse step and estimates its mean with a single MPPI update centered at the diffusion reverse mean. For differentiable costs, GRACE recovers conventional gradient guidance under a first-order, matched-covariance approximation. GRACE attains higher success rates than diffusion-based and sampling-based baselines in simulation. On a real 7-DoF manipulator, GRACE avoids a deployment-time obstacle that the unguided prior collides with in every trial. Code and experiment videos are available at https://anonymous.4open.science/w/grace-70BB/.