# Variational Distillation of Diffusion Policies into Mixture of Experts

arXiv: https://arxiv.org/abs/2406.12538 · HTML: https://mlsanity.com/paper/2406.12538/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 51 of its 68 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)
- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 30 of 51)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [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)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning](https://mlsanity.com/paper/1910.11956/) (2019)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation](https://mlsanity.com/paper/2405.07503/) (2024)
- [Efficient Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2305.20081/) (2023)

## Built on by (most cited first, 15 of 15)

- [DIME:Diffusion-Based Maximum Entropy Reinforcement Learning](https://mlsanity.com/paper/2502.02316/) (2025)
- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [Multi-student Diffusion Distillation for Better One-step Generators](https://mlsanity.com/paper/2410.23274/) (2024)
- [cVLA: Towards Efficient Camera-Space VLAs](https://mlsanity.com/paper/2507.02190/) (2025)
- [TS-DP: Reinforcement Speculative Decoding For Temporal Adaptive Diffusion Policy Acceleration](https://mlsanity.com/paper/2512.15773/) (2025)
- [Flexible Multitask Learning with Factorized Diffusion Policy](https://mlsanity.com/paper/2512.21898/) (2025)
- [Sparse ActionGen: Accelerating Diffusion Policy with Real-time Pruning](https://mlsanity.com/paper/2601.12894/) (2026)
- [Aggregation of Dependent Expert Distributions in Multimodal Variational Autoencoders](https://mlsanity.com/paper/2505.01134/) (2025)
- [Supervised Mixture-of-Experts for Surgical Grasping and Retraction](https://mlsanity.com/paper/2601.21971/) (2026)
- [Trust-Region Diffusion Policies for Massively Parallel On-Policy RL](https://mlsanity.com/paper/2606.15260/) (2026)
- [Diffusion Policy with Bayesian Expert Selection for Active Multi-Target Tracking](https://mlsanity.com/paper/2604.03404/) (2026)
- [Test-time Sparsity for Extreme Fast Action Diffusion](https://mlsanity.com/paper/2605.13316/) (2026)
- [CoRDE: Concept-Prior Routed Diffusion Experts for Structural Generalization in Robot Manipulation](https://mlsanity.com/paper/2606.21935/) (2026)
- [RoamFlow: Reinforcement-Aligned One-Step Action MeanFlow Policy for Image-Goal Navigation](https://mlsanity.com/paper/2606.29934/) (2026)
- [Beyond Independence: Learning Correlated Views for Variational Incomplete Multi-View Clustering](https://mlsanity.com/paper/2608.15757/) (2026)

## Abstract (arXiv)

This work introduces Variational Diffusion Distillation (VDD), a novel method that distills denoising diffusion policies into Mixtures of Experts (MoE) through variational inference. Diffusion Models are the current state-of-the-art in generative modeling due to their exceptional ability to accurately learn and represent complex, multi-modal distributions. This ability allows Diffusion Models to replicate the inherent diversity in human behavior, making them the preferred models in behavior learning such as Learning from Human Demonstrations (LfD). However, diffusion models come with some drawbacks, including the intractability of likelihoods and long inference times due to their iterative sampling process. The inference times, in particular, pose a significant challenge to real-time applications such as robot control. In contrast, MoEs effectively address the aforementioned issues while retaining the ability to represent complex distributions but are notoriously difficult to train. VDD is the first method that distills pre-trained diffusion models into MoE models, and hence, combines the expressiveness of Diffusion Models with the benefits of Mixture Models. Specifically, VDD leverages a decompositional upper bound of the variational objective that allows the training of each expert separately, resulting in a robust optimization scheme for MoEs. VDD demonstrates across nine complex behavior learning tasks, that it is able to: i) accurately distill complex distributions learned by the diffusion model, ii) outperform existing state-of-the-art distillation methods, and iii) surpass conventional methods for training MoE.