# Amortizing Trajectory Diffusion with Keyed Drift Fields

arXiv: https://arxiv.org/abs/2603.14056 · HTML: https://mlsanity.com/paper/2603.14056/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 33 of its 40 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Placed in

- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 33)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (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)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Critic Regularized Regression](https://mlsanity.com/paper/2006.15134/) (2020)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Model-Based Offline Planning](https://mlsanity.com/paper/2008.05556/) (2020)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Consistency Models as a Rich and Efficient Policy Class for Reinforcement Learning](https://mlsanity.com/paper/2309.16984/) (2023)
- [When does return-conditioned supervised learning work for offline reinforcement learning?](https://mlsanity.com/paper/2206.01079/) (2022)
- [Stein Variational Policy Gradient](https://mlsanity.com/paper/1704.02399/) (2017)

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

- [Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow](https://mlsanity.com/paper/2605.07727/) (2026)

## Abstract (arXiv)

Diffusion-based trajectory planners can synthesize rich, multimodal action sequences for offline reinforcement learning, but their iterative denoising incurs substantial inference-time cost, making closed-loop planning slow under tight compute budgets. We study the problem of achieving diffusion-like trajectory planning behavior with one-step inference, while retaining the ability to sample diverse candidate plans and condition on the current state in a receding-horizon control loop. Our key observation is that conditional trajectory generation fails under na"ive distribution-matching objectives when the similarity measure used to align generated trajectories with the dataset is dominated by unconstrained future dimensions. In practice, this causes attraction toward average trajectories, collapses action diversity, and yields near-static behavior. Our key insight is that conditional generative planning requires a conditioning-aware notion of neighborhood: trajectory updates should be computed using distances in a compact key space that reflects the condition, while still applying updates in the full trajectory space. Building on this, we introduce Keyed Drifting Policies (KDP), a one-step trajectory generator trained with a drift-field objective that attracts generated trajectories toward condition-matched dataset windows and repels them from nearby generated samples, using a stop-gradient drifted target to amortize iterative refinement into training. At inference, the resulting policy produces a full trajectory window in a single forward pass. Across standard RL benchmarks and real-time hardware deployments, KDP achieves strong performance with one-step inference and substantially lower planning latency than diffusion sampling. Project website, code and videos: https://keyed-drifting.github.io/