Junyu Chen, Franklin Liu, Moshu Xu, Lijian Yang
arXiv 18 Oct 2026 · Machine Learning
arXiv:2610.25495 · PDF · Extracted main text
Modeling limit order book (LOB) dynamics is central to market forecasting and execution-strategy evaluation. While diffusion models achieve strong empirical performance, existing LOB snapshot models typically lack a learned recurrent encoder and formal statistical guarantees. We introduce LOBGrad, a conditional DDPM framework for probabilistic LOB forecasting that combines an autoregressive RNN encoder with a diffusion-based generator. In particular, we establish an excess-risk oracle inequality for the one-step DDPM noise-prediction objective under exponential mixing and regularity assumptions. We further show that, under contractive dynamics, the dependence on the conditioning-window length can be reduced to a dependence on the latent-state dimension. Experiments on BTC/USDT, GOOGL, and META show that LOBGrad improves on its encoder-free diffusion ablation across all reported queue metrics and obtains competitive results against other baselines. It also reproduces the key stylized facts of LOB microstructure, and yields reasonably calibrated queue-based predictive intervals. A stylized downstream task illustrates the potential value of the generated forecasts.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Backhouse, Alfred and Li, Kang and Foerster, Jakob and Calinescu, An… (2025) Painting the Market: Generative Diffusion Models for Financial Limit Order Book Simulation and Forecasting | 0.928 | 4 | 3 | 100% |
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| 6 | Prata, Matteo and Masi, Giuseppe and Berti, Leonardo and Arrigoni, V… (2024) LOB-Based Deep Learning Models for Stock Price Trend Prediction: A Benchmark Study | 0.644 | 2 | 2 | 100% |
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| 8 | Bouchaud, Jean-Philippe and Bonart, Julius and Donier, Jonathan and… (2018) Trades, Quotes and Prices: Financial Markets Under the Microscope | 0.511 | 2 | 1 | 100% |
| 9 | Wang, Zhuohan and Ventre, Carmine (2025) DiffVolume: Diffusion Models for Volume Generation in Limit Order Books | 0.511 | 2 | 1 | 100% |
| 10 | Schäfer, Anton Maximilian and Zimmermann, Hans-Georg (2007) Recurrent Neural Networks Are Universal Approximators | 0.405 | 1 | 1 | 100% |
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