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

Jung Hun Phee, Tucker Balch · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.22727 · cited by 0 works (OpenAlex) · open-access PDF

French

Nous étudions la distribution conditionnelle du volume de commande limitée soumis au cours des cinq prochaines minutes, compte tenu du livre de commande actuel et du flux de commande récent. La tâche nécessite de capturer le placement des prix, le volume total et l'incertitude prédictive conjointement. Les pertes de diffusion de manière coordonnée ne tiennent pas explicitement compte du déplacement des prix, tandis que la normalisation des champs de masse unitaire supprime des informations sur le volume total. L'accord sur les statistiques de résumé sélectionnées n'établit pas non plus de fidélité à la distribution du champ commun. Nous introduisons OrderFlowDiT, un transformateur de diffusion conditionnelle pour l'offre non normalisée et les champs de demande de volume-à-prix, form

Machine translation (Meta M2M100); the English original follows.

Abstract

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. Agreement on selected summary statistics also does not establish fidelity to the joint field distribution. 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. We also develop a full-field evaluation framework that combines a transport cost sensitive to price placement and total volume with proper scoring rules and calibration diagnostics. 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. Both measures improve for every stock. These findings support incorporating price geometry and volume into generative modeling, with field accuracy and predictive uncertainty evaluated together.

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Topics: Scoring rule, Computer science, Probabilistic logic, Calibration, Bayesian probability, Joint probability distribution

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