Paper: arXiv 2602.03776

Authors: Zhuohan Wang, Carmine Ventre

Abstract

Modern generative models for limit order books (LOBs) can reproduce realistic market dynamics, but remain fundamentally passive: they either model what typically happens without accounting for hypothetical future market conditions, or they require interaction with another agent to explore alternative outcomes. This limits their usefulness for stress testing, scenario analysis, and decision-making. We propose \textbf{DiffLOB}, a regime-conditioned \textbf{Diff}usion model for controllable and counterfactual generation of \textbf{LOB} trajectories. DiffLOB explicitly conditions the generative process on future market regimes–including trend, volatility, liquidity, and order-flow imbalance, which enables the model to answer counterfactual queries of the form: ``If the future market regime were X instead of Y, how would the limit order book evolve?’’ Our systematic evaluation framework for counterfactual LOB generation consists of three criteria: (1) \textit{Controllable Realism}, measuring how well generated trajectories can reproduce marginal distributions, temporal dependence structure and regime variables; (2) \textit{Counterfactual validity}, testing whether interventions on future regimes induce consistent changes in the generated LOB dynamics; (3) \textit{Counterfactual usefulness}, assessing whether synthetic counterfactual trajectories improve downstream prediction of future market regimes.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative regime-conditioned diffusion framework (DiffLOB) for counterfactual limit order book generation. It achieves strong empirical rigor using high-frequency LOBSTER data across multiple assets, supported by a clearly structured score-based architecture and a publicly available GitHub repository.

Research Flowchart

  flowchart TD
    A[Research Goal: Counterfactual Generation in LOBs] --> B[Input Data: Limit Order Book Trajectories]
    B --> C[Method: DiffLOB Diffusion Model]
    C --> D[Conditioning: Future Market Regimes<br>Trend, Volatility, Liquidity, Imbalance]
    D --> E[Generation & Evaluation Framework]
    E --> F1[Controllable Realism:<br>Realistic Marginal & Temporal Dynamics]
    E --> F2[Counterfactual Validity:<br>Consistent Regime-Driven LOB Changes]
    E --> F3[Counterfactual Usefulness:<br>Enhanced Downstream Regime Prediction]

Cited References (93)

  1. Score-based generative modeling through stochastic differential equations (2021)
  2. Generative modeling by estimating gradients of the data distribution (2019)
  3. Denoising diffusion probabilistic models (2020)
  4. CSDI: Conditional score-based diffusion models for probabilistic time series imputation (2021)
  5. Diffusion models for adversarial purification (2022) — link
  6. Can Machines’ Learn’Finance? (2020)
  7. Deep unsupervised learning using nonequilibrium thermodynamics (2015)
  8. Improved denoising diffusion probabilistic models (2021)
and 85 more
  1. Denoising diffusion implicit models (2021)
  2. A connection between score matching and denoising autoencoders (2011)
  3. Elucidating the design space of diffusion-based generative models (2022)
  4. Diffusion models for time-series applications: a survey (2023)
  5. Autoregressive denoising diffusion models for multivariate probabilistic time series forecasting (2021)
  6. Scoregrad: Multivariate probabilistic time series forecasting with continuous energy-based generative models (2021) — link
  7. Generative time series forecasting with diffusion, denoise, and disentanglement (2022)
  8. Non-autoregressive conditional diffusion models for time series prediction (2023)
  9. Diffusion-based time series imputation and forecasting with structured state space models (2022)
  10. Regular time-series generation using sgm (2023) — link
  11. On the constrained time-series generation problem (2024)
  12. Forecasting stock market indices using padding-based fourier transform denoising and time series deep learning models (2021)
  13. Stock price prediction via discovering multi-frequency trading patterns (2017)
  14. Denoised Labels for Financial Time Series Data via Self-Supervised Learning (2022)
  15. Extracting and composing robust features with denoising autoencoders (2008)
  16. Prediction of the change points in stock markets using DAE-LSTM (2021)
  17. Deep Learning-based Integrated Framework for stock price movement prediction (2022)
  18. The Fourier transform and its applications (1986)
  19. Architectures for wavelet transforms: A survey (1996)
  20. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis (1998)
  21. A hybrid model for financial time series forecasting—integration of EWT, ARIMA with the improved ABC optimized ELM (2020)
  22. Forecasting East Asian indices futures via a novel hybrid of wavelet-PCA denoising and artificial neural network models (2016)
  23. A novel time-series model based on empirical mode decomposition for forecasting TAIEX (2014)
  24. Forecasting wavelet neural hybrid network with financial ensemble empirical mode decomposition and MCID evaluation (2021)
  25. Understanding diffusion models: A unified perspective (2022) — link
  26. Reverse-time diffusion equation models (1982)
  27. Modeling financial time-series with generative adversarial networks (2019)
  28. Empirical properties of asset returns: stylized facts and statistical issues (2001)
  29. Enriching financial datasets with generative adversarial networks (2019)
  30. Wasserstein generative adversarial networks (2017)
  31. Time-series generative adversarial networks (2019)
  32. Synthetic Data Augmentation for Deep Reinforcement Learning in Financial Trading (2022)
  33. Wavenet: A generative model for raw audio (2016) — link
  34. Conditional sig-wasserstein gans for time series generation (2020) — link
  35. Using generative adversarial networks to synthesize artificial financial datasets (2020) — link
  36. On convergence and stability of gans (2017) — link
  37. Generating realistic stock market order streams (2020)
  38. Total variation regularization for image denoising, I. Geometric theory (2008)
  39. Wavelet and FFT Based Image Denoising Using Non-Linear Filters. (2015)
  40. From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (1997)
  41. Lightgbm: A highly efficient gradient boosting decision tree (2017)
  42. Learning multiple stock trading patterns with temporal routing adaptor and optimal transport (2021)
  43. Listening to chaotic whispers: A deep learning framework for news-oriented stock trend prediction (2018)
  44. Stock movement prediction from tweets and historical prices (2018)
  45. Quant GANs: deep generation of financial time series (2020)
  46. Corrgan: Sampling realistic financial correlation matrices using generative adversarial networks (2020)
  47. Abides: Towards high-fidelity market simulation for AI research (2019) — link
  48. Efficiently modeling long sequences with structured state spaces (2021) — link
  49. Attention is all you need (2017)
  50. Guided diffusion model for adversarial purification (2022) — link
  51. DiffsFormer: A Diffusion Transformer on Stock Factor Augmentation — → 2402.06656
  52. Classifier-free diffusion guidance (2021)
  53. Diffusion models beat gans on image synthesis (2021)
  54. Styletime: Style transfer for synthetic time series generation (2022)
  55. Trades, quotes and prices: financial markets under the microscope (2018)
  56. Limit order books (2013)
  57. Towards realistic market simulations: a generative adversarial networks approach (2021)
  58. Generative AI for end-to-end limit order book modelling: A token-level autoregressive generative model of message flow using a deep state space network (2023)
  59. Limit order book simulation with generative adversarial networks (2023)
  60. A stochastic model for order book dynamics (2010)
  61. Hawkes processes in finance (2015)
  62. Modelling financial high frequency data using point processes (2009)
  63. An agent based model of the E-Mini S&P 500 applied to Flash Crash analysis (2012)
  64. Quantifying reflexivity in financial markets: Toward a prediction of flash crashes (2012)
  65. ABIDES-gym: gym environments for multi-agent discrete event simulation and application to financial markets (2021)
  66. How to evaluate trading strategies: Single agent market replay or multiple agent interactive simulation? (2019) — link
  67. A generative model of a limit order book using recurrent neural networks (2023)
  68. Film: Visual reasoning with a general conditioning layer (2018)
  69. Lobster: Limit order book reconstruction system (2011)
  70. Deep learning (2016)
  71. Adam: A Method for Stochastic Optimization (2015)
  72. A Financial Time Series Denoiser Based on Diffusion Models (2024)
  73. Diffusion variational autoencoder for tackling stochasticity in multi-step regression stock price prediction — → 2309.00073
  74. Denoising Diffusion Probabilistic Model for Realistic Financial Correlation Matrices (2024)
  75. WaveNet: A Generative Model for Raw Audio (2016)
  76. Tutorial on diffusion models for imaging and vision (2024)
  77. Deep limit order book forecasting: a microstructural guide (2025)
  78. HLOB–Information persistence and structure in limit order books (2025)
  79. MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model (2025)
  80. DiffVolume: Diffusion Models for Volume Generation in Limit Order Books (2025)
  81. CoFinDiff: Controllable Financial Diffusion Model for Time Series Generation (2025)
  82. TRADES: Generating Realistic Market Simulations with Diffusion Models (2025)
  83. Norm-Salvaged Embedding: Improving Condition Alignment of Synthetic Time Series Generation in Finance (2025)
  84. Adding conditional control to text-to-image diffusion models (2023)
  85. Learning structured output representation using deep conditional generative models (2015)

2 of 93 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.