# Score and Distribution Matching Policy: Advanced Accelerated Visuomotor Policies via Matched Distillation

arXiv: https://arxiv.org/abs/2412.09265 · HTML: https://mlsanity.com/paper/2412.09265/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 53 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 30 of 50)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [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)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [robosuite: A Modular Simulation Framework and Benchmark for Robot Learning](https://mlsanity.com/paper/2009.12293/) (2020)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [TinyVLA: Towards Fast, Data-Efficient Vision-Language-Action Models for Robotic Manipulation](https://mlsanity.com/paper/2409.12514/) (2024)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)

## Built on by (most cited first, 13 of 13)

- [ManiFlow: A General Robot Manipulation Policy via Consistency Flow Training](https://mlsanity.com/paper/2509.01819/) (2025)
- [CEED-VLA: Consistency Vision-Language-Action Model with Early-Exit Decoding](https://mlsanity.com/paper/2506.13725/) (2025)
- [FASTER: Rethinking Real-Time Flow VLAs](https://mlsanity.com/paper/2603.19199/) (2026)
- [Falcon: Fast Visuomotor Policies via Partial Denoising](https://mlsanity.com/paper/2503.00339/) (2025)
- [FreqPolicy: Efficient Flow-based Visuomotor Policy via Frequency Consistency](https://mlsanity.com/paper/2506.08822/) (2025)
- [One-Step Flow Policy: Self-Distillation for Fast Visuomotor Policies](https://mlsanity.com/paper/2603.12480/) (2026)
- [Sparse ActionGen: Accelerating Diffusion Policy with Real-time Pruning](https://mlsanity.com/paper/2601.12894/) (2026)
- [Ada3Drift: Adaptive Training-Time Drifting for One-Step 3D Visuomotor Robotic Manipulation](https://mlsanity.com/paper/2603.11984/) (2026)
- [ForeDiffusion: Foresight-Conditioned Diffusion Policy via Future View Construction for Robot Manipulation](https://mlsanity.com/paper/2601.12925/) (2026)
- [PRISM: Performer RS-IMLE for Single-pass Multisensory Imitation Learning](https://mlsanity.com/paper/2602.02396/) (2026)
- [FocalPolicy: Frequency-Optimized Chunking and Locally Anchored Flow Matching for Coherent Visuomotor Policy](https://mlsanity.com/paper/2605.15944/) (2026)
- [DriftOPD: Sequence-Level Reverse-KL Distillation for One-Step VLA Policies](https://mlsanity.com/paper/2610.00317/) (2026)
- [FastOPD: On-Policy Distillation for Lightweight VLA Deployment](https://mlsanity.com/paper/2610.02832/) (2026)

## Abstract (arXiv)

Visual-motor policy learning has advanced with architectures like diffusion-based policies, known for modeling complex robotic trajectories. However, their prolonged inference times hinder high-frequency control tasks requiring real-time feedback. While consistency distillation (CD) accelerates inference, it introduces errors that compromise action quality. To address these limitations, we propose the Score and Distribution Matching Policy (SDM Policy), which transforms diffusion-based policies into single-step generators through a two-stage optimization process: score matching ensures alignment with true action distributions, and distribution matching minimizes KL divergence for consistency. A dual-teacher mechanism integrates a frozen teacher for stability and an unfrozen teacher for adversarial training, enhancing robustness and alignment with target distributions. Evaluated on a 57-task simulation benchmark, SDM Policy achieves a 6x inference speedup while having state-of-the-art action quality, providing an efficient and reliable framework for high-frequency robotic tasks.