One-Step Generative Surrogate Models via Block-Triangular Joint Drifting
Abstract
Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current state. Standard trajectory data, however, typically provide only one realized next state for each observed current state and therefore do not provide an empirical approximation of the corresponding conditional distribution over possible next states. We introduce block-triangular joint drifting, which instead applies a projected drift field to the empirically accessible joint distribution of consecutive states. Importantly, the block-triangular architecture preserves the current-state marginal while making its second component a direct sampler of the conditional distribution of possible next states. The resulting surrogate generates stochastic trajectories with one model evaluation per time step, without auxiliary generative steps between time steps. Numerical experiments demonstrate accurate marginal and trajectory-dependent statistics and favorable accuracy-cost tradeoffs compared with deterministic, diffusion-, flow-, and distillation-based generative surrogate models.
Related
- Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration
- A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices
- Randomized inexact block triangular preconditioners for double saddle-point systems in PDE-constrained optimization
- Limits of Stochastic Semigroups and Block-Triangular Majorisation
- On the index of an anti-triangular block matrix
BibTeX
@misc{geissler2026onestep,
title = {{One-Step Generative Surrogate Models via Block-Triangular Joint Drifting}},
author = {Nicholas Geissler and Shreya Jha and Ricardo Baptista and Benjamin Peherstorfer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26435},
eprint = {2609.26435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26435},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - One-Step Generative Surrogate Models via Block-Triangular Joint Drifting
AU - Nicholas Geissler
AU - Shreya Jha
AU - Ricardo Baptista
AU - Benjamin Peherstorfer
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26435
UR - https://arxiv.org/abs/2609.26435
AB - Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current state. Standard trajectory data, however, typically provide only one realized next state for each observed current state and therefore do not provide an empirical approximation of the corresponding conditional distribution over possible next states. We introduce block-triangular joint drifting, which instead applies a projected drift field to the empirically accessible joint distribution of consecutive states. Importantly, the block-triangular architecture preserves the current-state marginal while making its second component a direct sampler of the conditional distribution of possible next states. The resulting surrogate generates stochastic trajectories with one model evaluation per time step, without auxiliary generative steps between time steps. Numerical experiments demonstrate accurate marginal and trajectory-dependent statistics and favorable accuracy-cost tradeoffs compared with deterministic, diffusion-, flow-, and distillation-based generative surrogate models.
ER -