# Constraint-Aware Diffusion Priors for High-Fidelity and Versatile Quadruped Locomotion

arXiv: https://arxiv.org/abs/2605.08804 · HTML: https://mlsanity.com/paper/2605.08804/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 9 May 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Real-world robot offline RL](https://mlsanity.com/offlinerl/real-world-robot-offline-rl/)
- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 29 of 29)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Learning Agile Robotic Locomotion Skills by Imitating Animals](https://mlsanity.com/paper/2004.00784/) (2020)
- [Speech Gesture Generation from the Trimodal Context of Text, Audio, and Speaker Identity](https://mlsanity.com/paper/2009.02119/) (2020)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots](https://mlsanity.com/paper/2306.14874/) (2023)
- [Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior](https://mlsanity.com/paper/2212.03238/) (2022)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [CALM: Conditional Adversarial Latent Models for Directable Virtual Characters](https://mlsanity.com/paper/2305.02195/) (2023)
- [Adversarial Motion Priors Make Good Substitutes for Complex Reward Functions](https://mlsanity.com/paper/2203.15103/) (2022)
- [Diffusion Reward: Learning Rewards via Conditional Video Diffusion](https://mlsanity.com/paper/2312.14134/) (2023)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [Learning Agile Skills via Adversarial Imitation of Rough Partial Demonstrations](https://mlsanity.com/paper/2206.11693/) (2022)
- [Advanced Skills through Multiple Adversarial Motion Priors in Reinforcement Learning](https://mlsanity.com/paper/2203.14912/) (2022)
- [Safe Reinforcement Learning for Legged Locomotion](https://mlsanity.com/paper/2203.02638/) (2022)
- [Track Any Motions under Any Disturbances](https://mlsanity.com/paper/2509.13833/) (2025)
- [Symmetry Considerations for Learning Task Symmetric Robot Policies](https://mlsanity.com/paper/2403.04359/) (2024)
- [Diffusion-Reward Adversarial Imitation Learning](https://mlsanity.com/paper/2405.16194/) (2024)
- [SoloParkour: Constrained Reinforcement Learning for Visual Locomotion from Privileged Experience](https://mlsanity.com/paper/2409.13678/) (2024)
- [SPiDR: A Simple Approach for Zero-Shot Safety in Sim-to-Real Transfer](https://mlsanity.com/paper/2509.18648/) (2025)
- [Coordinated Humanoid Robot Locomotion with Symmetry Equivariant Reinforcement Learning Policy](https://mlsanity.com/paper/2508.01247/) (2025)
- [Learning Multi-Skill Legged Locomotion Using Conditional Adversarial Motion Priors](https://mlsanity.com/paper/2509.21810/) (2025)
- [BarlowWalk: Self-supervised Representation Learning for Legged Robot Terrain-adaptive Locomotion](https://mlsanity.com/paper/2508.00939/) (2025)

## Built on by (most cited first, 1 of 1)

- [Behavior Foundations for Quadruped Robots: ABot-C0 Technical Report](https://mlsanity.com/paper/2607.07370/) (2026)

## Abstract (arXiv)

Reinforcement learning combined with imitation learning has significantly advanced biomimetic quadrupedal locomotion. However, scaling these frameworks to massive, multi-source datasets exposes fundamental bottlenecks. First, traditional GAN-based discriminators are prone to mode collapse, struggling to capture diverse motion distributions from uncurated datasets. Second, existing kinematic priors suffer from out-of-distribution (OOD) tracking conflicts, leading to severe unintended heading drifts during complex maneuvers. Furthermore, deploying unconstrained priors to physical hardware poses critical safety risks by disregarding actuator dynamics. To overcome these challenges, we propose Diff-CAST (Diffusion-guided Constraint-Aware Symmetric Tracking), a novel motion prior framework leveraging the multi-modal distribution modeling capabilities of diffusion models for stylistic rewards. Diff-CAST effectively replaces traditional GAN discriminators, unlocking robust data scaling on heterogeneous collections. To ensure high-fidelity intent execution and reliable real-world deployment, we introduce a comprehensive Sim2Real architecture integrating Symmetric Augmented Command Conditioning (SACC) for drift-free tracking, and Constrained RL for hardware safety. Experiments on a quadruped demonstrate that Diff-CAST mitigates mode collapse, enables seamless transitions between diverse skills, and ensures robust, hardware-compliant locomotion.