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

arXiv: https://arxiv.org/abs/2607.16238 · HTML: https://mlsanity.com/paper/2607.16238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 24 of its 57 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator](https://mlsanity.com/paper/2408.02965/) (2024)
- [StressNet: Deep Learning to Predict Stress With Fracture Propagation in Brittle Materials](https://mlsanity.com/paper/2011.10227/) (2020)
- [Reconstruct-and-Generate Diffusion Model for Detail-Preserving Image Denoising](https://mlsanity.com/paper/2309.10714/) (2023)
- [Uni-3DAD: GAN-Inversion Aided Universal 3D Anomaly Detection on Model-free Products](https://mlsanity.com/paper/2408.16201/) (2024)
- [NP-ODE: Neural Process Aided Ordinary Differential Equations for Uncertainty Quantification of Finite Element Analysis](https://mlsanity.com/paper/2012.06914/) (2020)
- [Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolations](https://mlsanity.com/paper/2510.05351/) (2025)
- [Quantum Safe-Set Bayesian Optimization for Quality Improvement in Fuselage Assembly](https://mlsanity.com/paper/2511.22090/) (2025)

## Abstract (arXiv)

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.