# Learnable Fractional Reaction-Diffusion Dynamics for Under-Display ToF Imaging and Beyond

arXiv: https://arxiv.org/abs/2511.01704 · HTML: https://mlsanity.com/paper/2511.01704/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 26 of 26)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Non-Local Spatial Propagation Network for Depth Completion](https://mlsanity.com/paper/2007.10042/) (2020)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Learning Depth with Convolutional Spatial Propagation Network](https://mlsanity.com/paper/1810.02695/) (2018)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Interpolated Convolutional Networks for 3D Point Cloud Understanding](https://mlsanity.com/paper/1908.04512/) (2019)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Image Restoration for Under-Display Camera](https://mlsanity.com/paper/2003.04857/) (2020)
- [Guided Depth Super-Resolution by Deep Anisotropic Diffusion](https://mlsanity.com/paper/2211.11592/) (2022)
- [Removing Diffraction Image Artifacts in Under-Display Camera via Dynamic Skip Connection Network](https://mlsanity.com/paper/2104.09556/) (2021)
- [Tackling 3D ToF Artifacts Through Learning and the FLAT Dataset](https://mlsanity.com/paper/1807.10376/) (2018)
- [Generating Aligned Pseudo-Supervision from Non-Aligned Data for Image Restoration in Under-Display Camera](https://mlsanity.com/paper/2304.06019/) (2023)
- [Deep End-to-End Alignment and Refinement for Time-of-Flight RGB-D Module](https://mlsanity.com/paper/1909.07623/) (2019)
- [Joint Graph-based Depth Refinement and Normal Estimation](https://mlsanity.com/paper/1912.01306/) (2019)
- [Neural Field Convolutions by Repeated Differentiation](https://mlsanity.com/paper/2304.01834/) (2023)
- [Very Power Efficient Neural Time-of-Flight](https://mlsanity.com/paper/1812.08125/) (2018)
- [CUF: Continuous Upsampling Filters](https://mlsanity.com/paper/2210.06965/) (2022)
- [SMPConv: Self-moving Point Representations for Continuous Convolution](https://mlsanity.com/paper/2304.02330/) (2023)
- [Depth Super-Resolution from Explicit and Implicit High-Frequency Features](https://mlsanity.com/paper/2303.09307/) (2023)

## Built on by (most cited first, 1 of 1)

- [TailProp: content-adaptive light- and heavy-tailed propagation for vision](https://mlsanity.com/paper/2609.11081/) (2026)

## Abstract (arXiv)

Under-display ToF imaging aims to achieve accurate depth sensing through a ToF camera placed beneath a screen panel. However, transparent OLED (TOLED) layers introduce severe degradations-such as signal attenuation, multi-path interference (MPI), and temporal noise-that significantly compromise depth quality. To alleviate this drawback, we propose Learnable Fractional Reaction-Diffusion Dynamics (LFRD2), a hybrid framework that combines the expressive power of neural networks with the interpretability of physical modeling. Specifically, we implement a time-fractional reaction-diffusion module that enables iterative depth refinement with dynamically generated differential orders, capturing long-term dependencies. In addition, we introduce an efficient continuous convolution operator via coefficient prediction and repeated differentiation to further improve restoration quality. Experiments on four benchmark datasets demonstrate the effectiveness of our approach. The code is publicly available at https://github.com/wudiqx106/LFRD2.