# Diffusion-corrected Autoregressive Fourier Neural Operator for Droplet Evolution Prediction

> Source: <https://arxiv.org/abs/2607.16238>
> Published: 2026-07-21 04:00:00+00:00

arXiv:2607.16238v1 Announce Type: new
Abstract: Predicting droplet evolution in material jetting, or Inkjet Printing (IJP), is essential for maintaining printing quality. However, long-horizon forecasts remain challenging due to error accumulation and the complex coupling of process variables. In this work, we introduce the Diffusion-corrected Auto-Regressive Fourier Neural Operator (DiffARFNO), a two-stage framework that combines an autoregressive Fourier-MIONet with a conditional Denoising Diffusion Implicit Model (DDIM) corrector. Fourier-MIONet is trained as a coarse predictor and deployed autoregressively for long-horizon forecasting. In the second stage, a DDIM-based conditional corrector refines the coarse prediction within each sliding window through efficient iterative denoising. By combining coarse predictions from Fourier-MIONet with a DDIM corrector that restores fine details, DiffARFNO aims to provide high-fidelity predictions for long-horizon forecasts. Extensive experiments on droplet datasets from ANSYS Fluent demonstrate that DiffARFNO significantly outperforms existing state-of-the-art models.