Painting the market: generative diffusion models for financial limit order book simulation and forecasting

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Painting the market: generative diffusion models for financial limit order book simulation and forecasting

Alfred Backhouse
Kang Li
Jakob Foerster
Anisoara Calinescu
Stefan Zohren
Published on 9/5/2025
Equities
Derivatives
Machine learning
Deep learning
High frequency trading
Backtesting
AI

This paper introduces a novel approach for generative modeling of limit order book (LOB) data by converting LOB states into a structured image format and applying diffusion models with inpainting. The method leverages spatio-temporal inductive biases through a convolutional UNet backbone, enabling parallel generation of long sequences and avoiding error accumulation common in autoregressive models. The authors contribute to the LOB-Bench benchmark to allow fair comparison between models using Level-2 (order book only) and Level-3 (including message data) inputs. Despite using only Level-2 data, the proposed model achieves state-of-the-art performance on GOOG stock under Wasserstein loss and competitive results under L1 loss, outperforming existing methods like LOBS5 on certain metrics. However, performance on INTC (a large-tick stock) is weaker due to sparse signal, leading to mode collapse. Ablation studies show that inference speed can be significantly improved with minimal performance loss by reducing sampling steps, highlighting the method's efficiency. The work demonstrates that diffusion-based image generation is a promising paradigm for financial LOB simulation, particularly when global distributional similarity is prioritized over local fidelity. Future directions include latent-space diffusion, conditional generation, and improvements for large-tick stocks.

Highlights

  • 1Introduces a novel image-based representation of limit order book (LOB) data that better captures spatio-temporal structure.
  • 2Applies diffusion models with inpainting to generate future LOB states, enabling parallel generation and mitigating error accumulation.
  • 3Publicly contributes to LOB-Bench, enabling fair comparison between Level-2 and Level-3 generative models.
  • 4Achieves state-of-the-art performance on LOB-Bench for GOOG stock, despite using only Level-2 data.
  • 5Demonstrates that the method prioritizes global distributional similarity over local fidelity, excelling under Wasserstein loss.

Methods

  • M
    Image-based representation of LOB data: converts LOB states into a 2-channel image (prices and sizes) with temporal and price-level axes.
  • M
    Denoising diffusion probabilistic models (DDPM) with a UNet backbone for generative modeling.
  • M
    Inpainting technique: masks future timesteps as noise and uses historical context to generate future states.
  • M
    Evaluation using LOB-Bench benchmark with L1 and Wasserstein losses, and ablation studies on inference steps and generalizability.

Results

  • R
    On GOOG data, the model achieves state-of-the-art performance under Wasserstein loss and competitive performance under L1 loss compared to Level-3 models.
  • R
    On INTC data, the model exhibits mode collapse and underperforms, highlighting challenges with large-tick stocks.
  • R
    Reducing inference steps from 1000 to 10 yields minimal performance degradation, enabling fast parallel generation.
  • R
    The model struggles with generalizability across different stocks, as the GOOG-trained model performs poorly on INTC data.
  • R
    Qualitative analysis shows the model captures broad statistical properties (e.g., spread, imbalance) but underestimates high-volume orders.
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