# From Noise to Order: Learning to Rank via Denoising Diffusion

arXiv: https://arxiv.org/abs/2602.11453 · HTML: https://mlsanity.com/paper/2602.11453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 32 of its 79 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 32)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [Large Language Models are Effective Text Rankers with Pairwise Ranking Prompting](https://mlsanity.com/paper/2306.17563/) (2023)
- [Language Models are Realistic Tabular Data Generators](https://mlsanity.com/paper/2210.06280/) (2022)
- [Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space](https://mlsanity.com/paper/2310.09656/) (2023)
- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [Large language models can accurately predict searcher preferences](https://mlsanity.com/paper/2309.10621/) (2023)
- [Introducing LETOR 4.0 Datasets](https://mlsanity.com/paper/1306.2597/) (2013)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Recent Advances in Speech Language Models: A Survey](https://mlsanity.com/paper/2410.03751/) (2024)
- [Beyond Yes and No: Improving Zero-Shot LLM Rankers via Scoring Fine-Grained Relevance Labels](https://mlsanity.com/paper/2310.14122/) (2023)
- [CoDi: Co-evolving Contrastive Diffusion Models for Mixed-type Tabular Synthesis](https://mlsanity.com/paper/2304.12654/) (2023)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [IRGAN: A Minimax Game for Unifying Generative and Discriminative Information Retrieval Models](https://mlsanity.com/paper/1705.10513/) (2017)
- [Policy Learning for Fairness in Ranking](https://mlsanity.com/paper/1902.04056/) (2019)
- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [Evaluating Stochastic Rankings with Expected Exposure](https://mlsanity.com/paper/2004.13157/) (2020)
- [LLM4Rerank: LLM-based Auto-Reranking Framework for Recommendations](https://mlsanity.com/paper/2406.12433/) (2024)
- [SOS: Score-based Oversampling for Tabular Data](https://mlsanity.com/paper/2206.08555/) (2022)
- [Adversarial Sampling and Training for Semi-Supervised Information Retrieval](https://mlsanity.com/paper/1811.04155/) (2018)
- [A Survey on Diffusion Models for Recommender Systems](https://mlsanity.com/paper/2409.05033/) (2024)
- [Synthetic Test Collections for Retrieval Evaluation](https://mlsanity.com/paper/2405.07767/) (2024)
- [Not All Relevance Scores are Equal: Efficient Uncertainty and Calibration Modeling for Deep Retrieval Models](https://mlsanity.com/paper/2105.04651/) (2021)
- [DiSK: A Diffusion Model for Structured Knowledge](https://mlsanity.com/paper/2312.05253/) (2023)
- [Non-Imaging Medical Data Synthesis for Trustworthy AI: A Comprehensive Survey](https://mlsanity.com/paper/2209.09239/) (2022)
- [SynDL: A Large-Scale Synthetic Test Collection for Passage Retrieval](https://mlsanity.com/paper/2408.16312/) (2024)
- [Sociotechnical Implications of Generative Artificial Intelligence for Information Access](https://mlsanity.com/paper/2405.11612/) (2024)

## Abstract (arXiv)

In information retrieval (IR), learning-to-rank (LTR) methods have traditionally limited themselves to discriminative machine learning approaches that model the probability of the document being relevant to the query given some feature representation of the query-document pair. In this work, we propose an alternative denoising diffusion-based deep generative approach to LTR that instead models the full joint distribution over feature vectors and relevance labels. While in the discriminative setting, an over-parameterized ranking model may find different ways to fit the training data, we hypothesize that candidate solutions that can explain the full data distribution under the generative setting are better equipped to estimate relevance. With this motivation, we propose DiffusionRank that extends TabDiff, an existing denoising diffusion-based generative model for tabular datasets, to create generative equivalents of classical discriminative pointwise and pairwise LTR objectives. We conduct thorough empirical evaluation on four standard LTR datasets to demonstrate improvements from DiffusionRank models over their discriminative counterparts. Our work points to a rich space for future research exploration on how we can leverage ongoing advancements in deep generative modeling approaches, such as diffusion, for LTR. We made our code publicly available at https://github.com/sadjadeb/DiffusionRank.