OrderFlowDiT: Transport-Regularized Diffusion Transformer for Probabilistic Limit-Order Supply Forecasting

01 ABSTRACT

The authors study the conditional distribution of limit-order volume across price levels over the next five minutes given the current order book and recent order flow, arguing that price placement, total volume, and predictive uncertainty must be captured jointly. They propose OrderFlowDiT with an unbalanced optimal transport auxiliary loss; in the primary comparison on 30 U.S. equities and 1950 validation conditions, adding UOT reduces full-field transport cost by 45.8% and transport energy score by 26.1% relative to training with mean squared error alone, with improvements for every stock. The evaluation framework combines transport cost, proper scoring rules, and calibration diagnostics to assess field accuracy and predictive uncertainty together.

02 KEY FINDINGS

1. OrderFlowDiT uses a conditional diffusion Transformer to model unnormalized bid and ask volume-at-price fields, trained with an unbalanced optimal transport (UOT) auxiliary loss.
2. In the primary comparison across 30 U.S. equities and 1950 validation conditions, adding UOT reduces full-field transport cost by 45.8% and transport energy score by 26.1% relative to MSE-only training, with improvements for every stock.
3. The study proposes a full-field evaluation framework that combines a transport cost sensitive to price placement and total volume with proper scoring rules and calibration diagnostics to jointly assess field accuracy and predictive uncertainty.