# Efficient, Property-Aligned Fan-Out Retrieval via RL-Compiled Diffusion

arXiv: https://arxiv.org/abs/2603.06397 · HTML: https://mlsanity.com/paper/2603.06397/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 52 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Builds on (most cited first, 30 of 39)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
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- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Large-scale Contrastive Language-Audio Pretraining with Feature Fusion and Keyword-to-Caption Augmentation](https://mlsanity.com/paper/2211.06687/) (2022)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Transformer Memory as a Differentiable Search Index](https://mlsanity.com/paper/2202.06991/) (2022)
- [Document Expansion by Query Prediction](https://mlsanity.com/paper/1904.08375/) (2019)
- [Query Rewriting for Retrieval-Augmented Large Language Models](https://mlsanity.com/paper/2305.14283/) (2023)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [Autoregressive Search Engines: Generating Substrings as Document Identifiers](https://mlsanity.com/paper/2204.10628/) (2022)
- [A Neural Corpus Indexer for Document Retrieval](https://mlsanity.com/paper/2206.02743/) (2022)
- [MuLan: A Joint Embedding of Music Audio and Natural Language](https://mlsanity.com/paper/2208.12415/) (2022)
- [Learning Fashion Compatibility with Bidirectional LSTMs](https://mlsanity.com/paper/1707.05691/) (2017)
- [DeepRetrieval: Hacking Real Search Engines and Retrievers with Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2503.00223/) (2025)
- [How Does Generative Retrieval Scale to Millions of Passages?](https://mlsanity.com/paper/2305.11841/) (2023)
- [Learning to Rank in Generative Retrieval](https://mlsanity.com/paper/2306.15222/) (2023)
- [Query expansion techniques for information retrieval: A survey](https://mlsanity.com/paper/1708.00247/) (2017)
- [s3: You Don't Need That Much Data to Train a Search Agent via RL](https://mlsanity.com/paper/2505.14146/) (2025)
- [Cross-Modal Retrieval: A Systematic Review of Methods and Future Directions](https://mlsanity.com/paper/2308.14263/) (2023)
- [Scalable and Effective Generative Information Retrieval](https://mlsanity.com/paper/2311.09134/) (2023)

## Abstract (arXiv)

Many modern retrieval problems are set-valued: given a broad intent, the system must return a collection of results that optimizes higher-order properties (e.g., diversity, coverage, complementarity, coherence) while remaining grounded with respect to a fixed database. Set-valued objectives are typically non-decomposable and are not captured by existing supervised (query, content) datasets which only prioritize top-1 retrieval. Consequently, fan-out retrieval is often employed to generate diverse subqueries to retrieve item sets. While reinforcement learning (RL) can optimize set-level objectives via interaction, deploying an RL-tuned LLM for fan-out retrieval is prohibitively expensive at inference time. Conversely, diffusion-based generative retrieval enables efficient single-pass fan-out in embedding space, but requires objective-aligned training targets. To address these issues, we propose R4T (Retrieve-for-Train), which uses RL once as an objective transducer in a three-step process: (i) train a fan-out LLM with composite set-level rewards, (ii) synthesize objective-consistent training pairs, and (iii) train a lightweight diffusion retriever to model the conditional distribution of set-valued outputs. Across large-scale fashion and music benchmarks consisting of curated item sets, we show that R4T improves retrieval quality relative to strong baselines while reducing query-time fan-out latency by an order of magnitude.