# FLOWING: Implicit Neural Flows for Structure-Preserving Morphing

arXiv: https://arxiv.org/abs/2510.09537 · HTML: https://mlsanity.com/paper/2510.09537/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [GaussianAvatars: Photorealistic Head Avatars with Rigged 3D Gaussians](https://mlsanity.com/paper/2312.02069/) (2023)
- [Real-Time Intermediate Flow Estimation for Video Frame Interpolation](https://mlsanity.com/paper/2011.06294/) (2020)
- [NeRSemble: Multi-view Radiance Field Reconstruction of Human Heads](https://mlsanity.com/paper/2305.03027/) (2023)
- [XFeat: Accelerated Features for Lightweight Image Matching](https://mlsanity.com/paper/2404.19174/) (2024)
- [IFRNet: Intermediate Feature Refine Network for Efficient Frame Interpolation](https://mlsanity.com/paper/2205.14620/) (2022)
- [Image Generators with Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2011.13775/) (2020)
- [DiffMorpher: Unleashing the Capability of Diffusion Models for Image Morphing](https://mlsanity.com/paper/2312.07409/) (2023)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Vulnerability Analysis of Face Morphing Attacks from Landmarks and Generative Adversarial Networks](https://mlsanity.com/paper/2012.05344/) (2020)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [Exploring Differential Geometry in Neural Implicits](https://mlsanity.com/paper/2201.09263/) (2022)
- [Medical Image Registration via Neural Fields](https://mlsanity.com/paper/2206.03111/) (2022)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [Neural Implicit Surface Evolution](https://mlsanity.com/paper/2201.09636/) (2022)
- [Neural Implicit Morphing of Face Images](https://mlsanity.com/paper/2308.13888/) (2023)
- [LADIMO: Face Morph Generation through Biometric Template Inversion with Latent Diffusion](https://mlsanity.com/paper/2410.07988/) (2024)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)

## Built on by (most cited first, 3 of 3)

- [From Volume Rendering to 3D Gaussian Splatting: Theory and Applications](https://mlsanity.com/paper/2510.18101/) (2025)
- [Adaptive Training of INRs via Pruning and Densification](https://mlsanity.com/paper/2510.23943/) (2025)
- [Enhancing Single-Image Facial Demorphing using Multimodal Large Language Models](https://mlsanity.com/paper/2605.25442/) (2026)

## Abstract (arXiv)

Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit neural representations (INRs) for modeling such deformations, due to their meshlessness and differentiability; however, extracting coherent and accurate morphings from standard MLPs typically relies on costly regularizations, which often lead to unstable training and prevent effective feature alignment. To overcome these limitations, we propose FLOWING (FLOW morphING), a framework that recasts warping as the construction of a differential vector flow, naturally ensuring continuity, invertibility, and temporal coherence by encoding structural flow properties directly into the network architectures. This flow-centric approach yields principled and stable transformations, enabling accurate and structure-preserving morphing of both 2D images and 3D shapes. Extensive experiments across a range of applications - including face and image morphing, as well as Gaussian Splatting morphing - show that FLOWING achieves state-of-the-art morphing quality with faster convergence. Code and pretrained models are available at http://schardong.github.io/flowing.