# LRT-Diffusion: Calibrated Risk-Aware Guidance for Diffusion Policies

arXiv: https://arxiv.org/abs/2510.24983 · HTML: https://mlsanity.com/paper/2510.24983/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 17 of its 25 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## 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 / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [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)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Safe Policy Improvement with Baseline Bootstrapping](https://mlsanity.com/paper/1712.06924/) (2017)

## Abstract (arXiv)

Diffusion policies are competitive for offline reinforcement learning (RL) but are typically guided at sampling time by heuristics that lack a statistical notion of risk. We introduce LRT-Diffusion, a risk-aware sampling rule that treats each denoising step as a sequential hypothesis test between the unconditional prior and the state-conditional policy head. Concretely, we accumulate a log-likelihood ratio and gate the conditional mean with a logistic controller whose threshold tau is calibrated once under H0 to meet a user-specified Type-I level alpha. This turns guidance from a fixed push into an evidence-driven adjustment with a user-interpretable risk budget. Importantly, we deliberately leave training vanilla (two heads with standard epsilon-prediction) under the structure of DDPM. LRT guidance composes naturally with Q-gradients: critic-gradient updates can be taken at the unconditional mean, at the LRT-gated mean, or a blend, exposing a continuum from exploitation to conservatism. We standardize states and actions consistently at train and test time and report a state-conditional out-of-distribution (OOD) metric alongside return. On D4RL MuJoCo tasks, LRT-Diffusion improves the return-OOD trade-off over strong Q-guided baselines in our implementation while honoring the desired alpha. Theoretically, we establish level-alpha calibration, concise stability bounds, and a return comparison showing when LRT surpasses Q-guidance-especially when off-support errors dominate. Overall, LRT-Diffusion is a drop-in, inference-time method that adds principled, calibrated risk control to diffusion policies for offline RL.