# SDR: Set-Distance Rewards for Radiology Report Generation

arXiv: https://arxiv.org/abs/2606.00440 · HTML: https://mlsanity.com/paper/2606.00440/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Clinical and biomedical applications, one of 17 directions in LLM reasoning.
- Builds on 24 of its 27 references that are in the map.
- First posted on arXiv 30 May 2026.

## Placed in

- LLM reasoning / [Clinical and biomedical applications](https://mlsanity.com/lr/clinical-and-biomedical-applications/)

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Med-Flamingo: a Multimodal Medical Few-shot Learner](https://mlsanity.com/paper/2307.15189/) (2023)
- [MedVLM-R1: Incentivizing Medical Reasoning Capability of Vision-Language Models (VLMs) via Reinforcement Learning](https://mlsanity.com/paper/2502.19634/) (2025)
- [Med-R1: Reinforcement Learning for Generalizable Medical Reasoning in Vision-Language Models](https://mlsanity.com/paper/2503.13939/) (2025)
- [Clinically Accurate Chest X-Ray Report Generation](https://mlsanity.com/paper/1904.02633/) (2019)
- [Chain of Code: Reasoning with a Language Model-Augmented Code Emulator](https://mlsanity.com/paper/2312.04474/) (2023)
- [Dynamic Graph Enhanced Contrastive Learning for Chest X-ray Report Generation](https://mlsanity.com/paper/2303.10323/) (2023)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [MedReason: Eliciting Factual Medical Reasoning Steps in LLMs via Knowledge Graphs](https://mlsanity.com/paper/2504.00993/) (2025)
- [Multi-modal Understanding and Generation for Medical Images and Text via Vision-Language Pre-Training](https://mlsanity.com/paper/2105.11333/) (2021)
- [CT2Rep: Automated Radiology Report Generation for 3D Medical Imaging](https://mlsanity.com/paper/2403.06801/) (2024)
- [Entropy-Regularized Process Reward Model](https://mlsanity.com/paper/2412.11006/) (2024)
- [R-PRM: Reasoning-Driven Process Reward Modeling](https://mlsanity.com/paper/2503.21295/) (2025)
- [Towards a Holistic Framework for Multimodal Large Language Models in Three-dimensional Brain CT Report Generation](https://mlsanity.com/paper/2407.02235/) (2024)
- [ReXGradient-160K: A Large-Scale Publicly Available Dataset of Chest Radiographs with Free-text Reports](https://mlsanity.com/paper/2505.00228/) (2025)
- [Medical-VLBERT: Medical Visual Language BERT for COVID-19 CT Report Generation With Alternate Learning](https://mlsanity.com/paper/2108.05067/) (2021)
- [More Bang for the Buck: Process Reward Modeling with Entropy-Driven Uncertainty](https://mlsanity.com/paper/2503.22233/) (2025)

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

- [Discrete Diffusion Language Models for Interactive Radiology Report Drafting](https://mlsanity.com/paper/2607.01436/) (2026)
- [Transition-Aware best-of-N sampling for Longitudinal Chest X-ray Reports](https://mlsanity.com/paper/2606.28393/) (2026)
- [From Sampled Evidence to Radiology Reports: Objectives, Constraints, and Realization](https://mlsanity.com/paper/2610.17318/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards has rapidly advanced reasoning in vision--language models. However, for chest X-ray report generation, the standard rewards (i.e. exact-match accuracy and step-level processes) are incompatible because the reports consist of unordered and orthogonal findings, rather than a causal reasoning chain. We address this gap with a set-based view: each report is split into sentences and embedded by a frozen sentence transformer, yielding unordered embedding sets. We propose the use of set-to-set distances between generated and reference embeddings as continuous, permutation-invariant rewards. Across two datasets and three vision--language models (Qwen3-VL-2B/4B, Gemma3-4B), post-training with set-to-set distance based rewards via GRPO consistently outperforms supervised fine-tuning and exact-match GRPO on all headline metrics (BERTScore, RadGraph F1 and CheXbert F1 by average %6.80, %7.82 and %4.45 relative improvements respectively). The same set distances also enable test-time best-of-N selection: scoring candidates by their distance to training-report embeddings outperforms random selection on our trained models as well as three closed-source LLMs (Mistral-Small, Gemini-2.5 Flash-Lite, GPT-4o-mini) with on average %16.4 relative improvement on BERTScore. Used as a streaming signal, they support a more efficient form of test-time scaling: pruning low-scoring candidates mid-generation reduces generated tokens by over 50% while preserving the Findings quality of full best-of-N selection. Together these results establish set-distance rewards as a unified signal for both post-training and test-time scaling in chest X-ray report generation. Our code is publicly hrefhttps://anonymous.4open.science/r/Set-Distance-Rewards-CXR-BFDAavailable.