# DiffLOB: Diffusion Models for Counterfactual Generation in Limit Order Books

arXiv: https://arxiv.org/abs/2602.03776 · HTML: https://mlsanity.com/paper/2602.03776/

## Key facts

- Cited by 2 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 20 of its 30 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## 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, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Towards Realistic Market Simulations: a Generative Adversarial Networks Approach](https://mlsanity.com/paper/2110.13287/) (2021)
- [MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model](https://mlsanity.com/paper/2409.07486/) (2024)
- [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](https://mlsanity.com/paper/2309.00638/) (2023)
- [Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction](https://mlsanity.com/paper/2309.00073/) (2023)
- [HLOB -- Information Persistence and Structure in Limit Order Books](https://mlsanity.com/paper/2405.18938/) (2024)
- [Deep Limit Order Book Forecasting](https://mlsanity.com/paper/2403.09267/) (2024)
- [A Financial Time Series Denoiser Based on Diffusion Model](https://mlsanity.com/paper/2409.02138/) (2024)
- [TRADES: Generating Realistic Market Simulations with Diffusion Models](https://mlsanity.com/paper/2502.07071/) (2025)
- [DiffVolume: Diffusion Models for Volume Generation in Limit Order Books](https://mlsanity.com/paper/2508.08698/) (2025)

## Built on by (most cited first, 2 of 2)

- [LOB-ID: Evaluating Synthetic Market Data by Inception Distances](https://mlsanity.com/paper/2608.13082/) (2026)
- [FlowLOB: Efficient and Controllable Limit Order Book Generation with Flow Matching](https://mlsanity.com/paper/2608.13096/) (2026)

## Abstract (arXiv)

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 DiffLOB, a regime-conditioned Diffusion model for controllable and counterfactual generation of 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) textitControllable Realism, measuring how well generated trajectories can reproduce marginal distributions, temporal dependence structure and regime variables; (2) textitCounterfactual validity, testing whether interventions on future regimes induce consistent changes in the generated LOB dynamics; (3) textitCounterfactual usefulness, assessing whether synthetic counterfactual trajectories improve downstream prediction of future market regimes.