# Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction

arXiv: https://arxiv.org/abs/2309.00073 · HTML: https://mlsanity.com/paper/2309.00073/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 62 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Temporal Relational Ranking for Stock Prediction](https://mlsanity.com/paper/1809.09441/) (2018)
- [Adversarial score matching and improved sampling for image generation](https://mlsanity.com/paper/2009.05475/) (2020)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [Listening to Chaotic Whispers: A Deep Learning Framework for News-oriented Stock Trend Prediction](https://mlsanity.com/paper/1712.02136/) (2017)
- [Risk-Averse Trust Region Optimization for Reward-Volatility Reduction](https://mlsanity.com/paper/1912.03193/) (2019)
- [Learning Hierarchical Priors in VAEs](https://mlsanity.com/paper/1905.04982/) (2019)
- [Neural Empirical Bayes](https://mlsanity.com/paper/1903.02334/) (2019)
- [Learning Multiple Stock Trading Patterns with Temporal Routing Adaptor and Optimal Transport](https://mlsanity.com/paper/2106.12950/) (2021)
- [Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matching](https://mlsanity.com/paper/1910.07762/) (2019)
- [NumHTML: Numeric-Oriented Hierarchical Transformer Model for Multi-task Financial Forecasting](https://mlsanity.com/paper/2201.01770/) (2022)
- [Multi-Graph Convolutional Network for Relationship-Driven Stock Movement Prediction](https://mlsanity.com/paper/2005.04955/) (2020)
- [Learning to Discover Sparse Graphical Models](https://mlsanity.com/paper/1605.06359/) (2016)
- [Style Transfer with Time Series: Generating Synthetic Financial Data](https://mlsanity.com/paper/1906.03232/) (2019)
- [Denoised Labels for Financial Time-Series Data via Self-Supervised Learning](https://mlsanity.com/paper/2112.10139/) (2021)
- [Theoretically Motivated Data Augmentation and Regularization for Portfolio Construction](https://mlsanity.com/paper/2106.04114/) (2021)

## Built on by (most cited first, 10 of 10)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [FinCast: A Foundation Model for Financial Time-Series Forecasting](https://mlsanity.com/paper/2508.19609/) (2025)
- [MANA-Net: Mitigating Aggregated Sentiment Homogenization with News Weighting for Enhanced Market Prediction](https://mlsanity.com/paper/2409.05698/) (2024)
- [FinVision: A Multi-Agent Framework for Stock Market Prediction](https://mlsanity.com/paper/2411.08899/) (2024)
- [Learning Universal Multi-level Market Irrationality Factors to Improve Stock Return Forecasting](https://mlsanity.com/paper/2502.04737/) (2025)
- [DiffLOB: Diffusion Models for Counterfactual Generation in Limit Order Books](https://mlsanity.com/paper/2602.03776/) (2026)
- [DiffVolume: Diffusion Models for Volume Generation in Limit Order Books](https://mlsanity.com/paper/2508.08698/) (2025)
- [From Local Patterns to Global Understanding: Cross-Stock Trend Integration for Enhanced Predictive Modeling](https://mlsanity.com/paper/2505.16573/) (2025)
- [F2Agent: Financial Fusion of Agentic Intelligence for Multimodal Trading](https://mlsanity.com/paper/2608.05668/) (2026)
- [Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolios](https://mlsanity.com/paper/2609.35086/) (2026)

## Abstract (arXiv)

Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility, allowing financial institutions to price and hedge derivatives, and banks to quantify the risk in their trading books. Additionally, most financial regulators also require a liquidity horizon of several days for institutional investors to exit their risky assets, in order to not materially affect market prices. However, the task of multi-step stock price prediction is challenging, given the highly stochastic nature of stock data. Current solutions to tackle this problem are mostly designed for single-step, classification-based predictions, and are limited to low representation expressiveness. The problem also gets progressively harder with the introduction of the target price sequence, which also contains stochastic noise and reduces generalizability at test-time. To tackle these issues, we combine a deep hierarchical variational-autoencoder (VAE) and diffusion probabilistic techniques to do seq2seq stock prediction through a stochastic generative process. The hierarchical VAE allows us to learn the complex and low-level latent variables for stock prediction, while the diffusion probabilistic model trains the predictor to handle stock price stochasticity by progressively adding random noise to the stock data. Our Diffusion-VAE (D-Va) model is shown to outperform state-of-the-art solutions in terms of its prediction accuracy and variance. More importantly, the multi-step outputs can also allow us to form a stock portfolio over the prediction length. We demonstrate the effectiveness of our model outputs in the portfolio investment task through the Sharpe ratio metric and highlight the importance of dealing with different types of prediction uncertainties.