ResearchResearch paperTraining & Scaling · Efficiency & Inference1 source · Oct 15, 2026

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

We introduce OrderFlowDiT, a conditional Diffusion Transformer for unnormalized bid and ask volume-at-price fields, trained with an unbalanced optimal-transport (UOT) auxiliary loss.

Key points

  • We study the conditional distribution of limit-order volume submitted over the next five minutes, given the current order book and recent order flow.
  • The task requires capturing price placement, total volume, and predictive uncertainty jointly.
  • Coordinate-wise diffusion losses do not explicitly account for price displacement, while normalizing fields to unit mass removes information about total volume.
  • In the primary comparison on 1950 validation conditions across 30 U.S. equities, adding UOT reduces full-field transport cost by 45.8% and the transport energy score by 26.1% relative to training with mean squared error alone.

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