# Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolios

arXiv: https://arxiv.org/abs/2609.35086 · HTML: https://mlsanity.com/paper/2609.35086/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
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- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [FinBERT: Financial Sentiment Analysis with Pre-trained Language Models](https://mlsanity.com/paper/1908.10063/) (2019)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem](https://mlsanity.com/paper/1706.10059/) (2017)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Fin-R1: A Large Language Model for Financial Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2503.16252/) (2025)
- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [Listening to Chaotic Whispers: A Deep Learning Framework for News-oriented Stock Trend Prediction](https://mlsanity.com/paper/1712.02136/) (2017)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling](https://mlsanity.com/paper/2404.12940/) (2024)
- [AlphaStock: A Buying-Winners-and-Selling-Losers Investment Strategy using Interpretable Deep Reinforcement Attention Networks](https://mlsanity.com/paper/1908.02646/) (2019)
- [Retrieval-Augmented Diffusion Models for Time Series Forecasting](https://mlsanity.com/paper/2410.18712/) (2024)
- [Learning to Generate Explainable Stock Predictions using Self-Reflective Large Language Models](https://mlsanity.com/paper/2402.03659/) (2024)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [Neural Diffusion Models](https://mlsanity.com/paper/2310.08337/) (2023)
- [Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction](https://mlsanity.com/paper/2309.00073/) (2023)
- [DiffsFormer: A Diffusion Transformer on Stock Factor Augmentation](https://mlsanity.com/paper/2402.06656/) (2024)
- [NGAT: A Node-level Graph Attention Network for Long-term Stock Prediction](https://mlsanity.com/paper/2507.02018/) (2025)

## Abstract (arXiv)

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.