# Neuroexplicit Diffusion Models for Inpainting of Optical Flow Fields

arXiv: https://arxiv.org/abs/2405.14599 · HTML: https://mlsanity.com/paper/2405.14599/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 23 May 2024.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [GMFlow: Learning Optical Flow via Global Matching](https://mlsanity.com/paper/2111.13680/) (2021)
- [FlowFormer: A Transformer Architecture for Optical Flow](https://mlsanity.com/paper/2203.16194/) (2022)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.01217/) (2023)
- [Connections between Numerical Algorithms for PDEs and Neural Networks](https://mlsanity.com/paper/2107.14742/) (2021)
- [Image Inpainting Using Wasserstein Generative Adversarial Imputation Network](https://mlsanity.com/paper/2106.15341/) (2021)
- [Inpainting-based Video Compression in FullHD](https://mlsanity.com/paper/2008.10273/) (2020)
- [Domain Decomposition Algorithms for Real-time Homogeneous Diffusion Inpainting in 4K](https://mlsanity.com/paper/2110.03946/) (2021)
- [Compressing Flow Fields with Edge-aware Homogeneous Diffusion Inpainting](https://mlsanity.com/paper/1906.12263/) (2019)

## Abstract (arXiv)

Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to generalize. At the other extreme, models designed from partial differential equations (PDEs) embed specialized domain knowledge into mathematical equations and usually rely on few manually chosen hyperparameters. This makes them transparent by construction and if designed and calibrated carefully, they can generalize well to unseen scenarios. In this paper, we show how to bring model- and data-driven approaches together by combining the explicit PDE-based approaches with convolutional neural networks to obtain the best of both worlds. We illustrate a joint architecture for the task of inpainting optical flow fields and show that the combination of model- and data-driven modeling leads to an effective architecture. Our model outperforms both fully explicit and fully data-driven baselines in terms of reconstruction quality, robustness and amount of required training data. Averaging the endpoint error across different mask densities, our method outperforms the explicit baselines by 11-27%, the GAN baseline by 47% and the Probabilisitic Diffusion baseline by 42%. With that, our method sets a new state of the art for inpainting of optical flow fields from random masks.