DiffLOB: Diffusion Models for Counterfactual Generation in Limit Order Books

This repository contains the official implementation of DiffLOB, a score-based diffusion framework for controllable and counterfactual generation of limit order book (LOB) trajectories under future market regime interventions.

DiffLOB explicitly conditions the generative process on future market regimes—including trend, volatility, liquidity, and order-flow imbalance—and enables direct counterfactual queries of the form:

“If the future market regime were different, how would the LOB evolve?”

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🔍 Overview

Existing generative models for limit order books primarily focus on reproducing realistic market dynamics, but remain fundamentally passive: they model what typically happens, rather than what would happen under hypothetical future conditions.

DiffLOB addresses this limitation by:

• Formulating LOB generation as a conditional score-based diffusion problem
• Explicitly introducing future market regimes as control variables
• Enabling counterfactual interventions without relying on agent-based interaction
• Demonstrating the usefulness of counterfactual trajectories for downstream tasks

Model architecture is shown by following graph:

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✨ Key Features

• Score-based diffusion model (VP-SDE) for LOB trajectories
• Explicit conditioning on future market regimes
• ControlNet-style control module for regime-aware intervention
• Two-stage training strategy for stable controllable generation
• Classifier-free guidance for flexible conditional sampling
• Ancestral sampling of the reverse-time SDE
• Joint modeling of price and volume dynamics
• Extensive evaluation on realism, counterfactual validity, and downstream usefulness

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🧠 Building Conditioning Variables

DiffLOB requires future market regime conditions to be precomputed before counterfactual sampling. These conditioning variables are constructed using the script:

python build_conds.py

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▶️ Running Training and Sampling Scripts

All training and sampling procedures are managed through scripts in the scripts/ directory. Run:

bash scripts/AMZN/diff_wavenet_motion_control.sh

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🎲 Sampling Examples

Below we show representative sampled LOB trajectory snippets generated by DiffLOB. Unless otherwise specified, figures are shown on AMZN.