# NormGuard: Reward-Preserving Norm Constraints in Flow-Matching Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.27771 · HTML: https://mlsanity.com/paper/2606.27771/

## 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 31 of its 46 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)
- 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 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [DiffusionNFT: Online Diffusion Reinforcement with Forward Process](https://mlsanity.com/paper/2509.16117/) (2025)
- [HPSv3: Towards Wide-Spectrum Human Preference Score](https://mlsanity.com/paper/2508.03789/) (2025)
- [Confronting Reward Model Overoptimization with Constrained RLHF](https://mlsanity.com/paper/2310.04373/) (2023)
- [Pref-GRPO: Pairwise Preference Reward-based GRPO for Stable Text-to-Image Reinforcement Learning](https://mlsanity.com/paper/2508.20751/) (2025)
- [RewardDance: Reward Scaling in Visual Generation](https://mlsanity.com/paper/2509.08826/) (2025)
- [Advantage Weighted Matching: Aligning RL with Pretraining in Diffusion Models](https://mlsanity.com/paper/2509.25050/) (2025)
- [GRPO-Guard: Mitigating Implicit Over-Optimization in Flow Matching via Regulated Clipping](https://mlsanity.com/paper/2510.22319/) (2025)
- [STIV: Scalable Text and Image Conditioned Video Generation](https://mlsanity.com/paper/2412.07730/) (2024)
- [Seeing Before Reasoning: A Unified Framework for Generalizable and Explainable Fake Image Detection](https://mlsanity.com/paper/2509.25502/) (2025)
- [GARDO: Reinforcing Diffusion Models without Reward Hacking](https://mlsanity.com/paper/2512.24138/) (2025)
- [RealGen: Photorealistic Text-to-Image Generation via Detector-Guided Rewards](https://mlsanity.com/paper/2512.00473/) (2025)
- [Flow-Factory: A Unified Framework for Reinforcement Learning in Flow-Matching Models](https://mlsanity.com/paper/2602.12529/) (2026)
- [RealDPO: Real or Not Real, that is the Preference](https://mlsanity.com/paper/2510.14955/) (2025)

## Abstract (arXiv)

Reinforcement learning (RL) post-training improves the reward alignment of flow-based generators, but often degrades perceptual quality in ways that are not captured by the reward proxy. We identify a simple structural signature of this drift: across three post-training methods (NFT, AWM, DPO), RL fine-tuning inflates the per-step velocity norm |vθ| by 5% to 15% relative to the reference. A form of norm inflation has been studied in classifier-free guidance (CFG), where rescaling the velocity back to a reference norm at inference time can mitigate the resulting artifacts. However, this inference-time correction does not transfer cleanly to RL: rescaling vθ to match |vref| at inference time neither improves reward nor fixes the quality degradation, because the inflation is co-adapted into the model weights. Furthermore, an adjoint sensitivity analysis shows that velocity magnitude rescaling carries no coherent first-order reward signal at the batch level, indicating that suppressing norm inflation is unlikely to remove a consistently reward-carrying component. Since inference-time renormalization fails while norm suppression carries no reward cost, training-time intervention is the appropriate strategy. Together, these findings motivate NormGuard, a hinge penalty that activates only when |vθ| exceeds |vref| and composes additively with any velocity-local base loss. Across two base models, three post-training methods, and two reward proxies, NormGuard consistently improves MLLM-judged image quality and forensic realism while preserving reward, with gains that amplify under few-step inference and are not explained by early stopping.