# Training Diffusion Policies via Prior-Mapping Co-Evolution

arXiv: https://arxiv.org/abs/2512.02581 · HTML: https://mlsanity.com/paper/2512.02581/

## Key facts

- Cited by 3 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 32 of its 47 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Deep reinforcement learning methods / [RL with diffusion and flow models](https://mlsanity.com/deeprl/rl-with-diffusion-and-flow-models/)

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [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)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [PLAS: Latent Action Space for Offline Reinforcement Learning](https://mlsanity.com/paper/2011.07213/) (2020)
- [Diffusion-based Reinforcement Learning via Q-weighted Variational Policy Optimization](https://mlsanity.com/paper/2405.16173/) (2024)
- [Flow Matching Policy Gradients](https://mlsanity.com/paper/2507.21053/) (2025)
- [ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learning](https://mlsanity.com/paper/2505.22094/) (2025)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs](https://mlsanity.com/paper/1902.10298/) (2019)
- [Learning Multimodal Behaviors from Scratch with Diffusion Policy Gradient](https://mlsanity.com/paper/2406.00681/) (2024)
- [Flow-Based Policy for Online Reinforcement Learning](https://mlsanity.com/paper/2506.12811/) (2025)
- [SAC Flow: Sample-Efficient Reinforcement Learning of Flow-Based Policies via Velocity-Reparameterized Sequential Modeling](https://mlsanity.com/paper/2509.25756/) (2025)

## Built on by (most cited first, 3 of 3)

- [Reparameterization Flow Policy Optimization](https://mlsanity.com/paper/2602.03501/) (2026)
- [FlowRL: A Taxonomy and Modular Framework for Reinforcement Learning with Diffusion Policies](https://mlsanity.com/paper/2603.27450/) (2026)
- [Flow Matching Policy Optimization with Mirror Descent and Entropy Constraints](https://mlsanity.com/paper/2603.17685/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) faces a persistent tension: policies that are stable to optimize (e.g., Gaussians) are often too simple to represent the multimodal action distributions required for complex control. Conversely, expressive generative policies -- such as diffusion and flow matching -- can be difficult to optimize in online RL due to intractable likelihoods and gradients propagating through long sampling chains. We address this tension with a key structural principle: decoupling optimization from generation. Building on this, we introduce GoRL (Generative Online Reinforcement Learning), an algorithm-agnostic framework that trains expressive policies from scratch by confining policy optimization to a tractable latent space while delegating action synthesis to a conditional generative decoder. Viewed as prior-mapping co-evolution, each stage first improves a tractable latent prior through RL and then consolidates the resulting behavior into a more expressive prior-to-action mapping. This two-timescale schedule, anchored by fixed-prior decoder refinement, enables stable optimization while continuously expanding expressiveness. Empirically, textscGoRL consistently outperforms unimodal and generative baselines across diverse continuous-control tasks. Notably, GoRL achieves returns exceeding 870 on HopperStand, more than 3* the strongest baseline; on high-dimensional humanoid tasks, it further outperforms the strongest non-GoRL baseline by over an order of magnitude.