Conditional Mean Flows for Frequency-Domain Scattered Wavefield Generation

Abstract

Frequency-domain wavefield modeling underpins seismic imaging and inversion, where repeated Helmholtz solutions become costly as velocity models, source locations, and frequencies vary. Neural operators learn mappings between physical fields, and their accuracy can decline outside the training distribution. Diffusion models learn wavefield distributions and generally require repeated sampling evaluations to produce accurate fields. A conditional mean flows model is introduced for complex scattered-wavefield generation. The analytical background wavefield serves as a condition alongside the velocity model, supplying spatially organized information about the source location and frequency. Learning the scattered wavefield avoids the point-source singularity in the target and supports generalization across these physical conditions. The model estimates the average transport velocity over a finite interval connecting Gaussian noise to the scattered field. This representation captures the accumulated displacement and permits both full-interval one-step generation and interval-partitioned sampling. Trained on OpenFWI, the model is evaluated on in-distribution and out-of-distribution velocity structures, frequency generalization, and inference efficiency. In most evaluated settings, one-step mean flows sampling achieves lower wavefield error than multi-step diffusion. Because each sampling step requires another network evaluation, accurate one-step generation also reduces inference time. These results indicate that mean flows can provide accurate and efficient frequency-domain scattered-wavefield generation.