# Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpening arXiv: https://arxiv.org/abs/2503.14975 ยท HTML: https://mlsanity.com/paper/2503.14975/ ## Key facts - Cited by 6 papers in the map (data through 14 Oct 2026). - Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. - Builds on 34 of its 65 references that are in the map. - First posted on arXiv 19 Mar 2025. ## Placed in - Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/) ## Builds on (most cited first, 30 of 34) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015) - [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016) - [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022) - [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016) - [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024) - [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024) - [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013) - [UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANs](https://mlsanity.com/paper/2311.09257/) (2023) - [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023) - [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022) - [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023) - [Align Your Steps: Optimizing Sampling Schedules in Diffusion Models](https://mlsanity.com/paper/2404.14507/) (2024) - [Dilated Neighborhood Attention Transformer](https://mlsanity.com/paper/2209.15001/) (2022) - [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024) - [textitJump Your Steps: Optimizing Sampling Schedule of Discrete Diffusion Models](https://mlsanity.com/paper/2410.07761/) (2024) - [Bespoke Solvers for Generative Flow Models](https://mlsanity.com/paper/2310.19075/) (2023) - [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022) - [Simple ReFlow: Improved Techniques for Fast Flow Models](https://mlsanity.com/paper/2410.07815/) (2024) - [Pansharpening via Detail Injection Based Convolutional Neural Networks](https://mlsanity.com/paper/1806.08898/) (2018) - [Optimal Transport for Unsupervised Denoising Learning](https://mlsanity.com/paper/2108.02574/) (2021) - [Existence, Duality, and Cyclical monotonicity for weak transport costs](https://mlsanity.com/paper/1809.05893/) (2018) - [SSDiff: Spatial-spectral Integrated Diffusion Model for Remote Sensing Pansharpening](https://mlsanity.com/paper/2404.11537/) (2024) ## Built on by (most cited first, 6 of 6) - [WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport](https://mlsanity.com/paper/2601.06810/) (2026) - [Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshots](https://mlsanity.com/paper/2605.00545/) (2026) - [WFR-MFM: One-Step Inference for Dynamic Unbalanced Optimal Transport](https://mlsanity.com/paper/2601.20606/) (2026) - [TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics](https://mlsanity.com/paper/2608.21070/) (2026) - [CC-Pan: Channel-wise Compression based Diffusion for Efficient Pan-Sharpening](https://mlsanity.com/paper/2602.04473/) (2026) - [Simulation-free Unbalanced Dynamic Optimal Transport with General Growth Penalty](https://mlsanity.com/paper/2609.04710/) (2026) ## Abstract (arXiv) Pansharpening, a pivotal task in remote sensing for fusing high-resolution panchromatic and multispectral imagery, has garnered significant research interest. Recent advancements employing diffusion models based on stochastic differential equations (SDEs) have demonstrated state-of-the-art performance. However, the inherent multi-step sampling process of SDEs imposes substantial computational overhead, hindering practical deployment. While existing methods adopt efficient samplers, knowledge distillation, or retraining to reduce sampling steps (e.g., from 1,000 to fewer steps), such approaches often compromise fusion quality. In this work, we propose the Optimal Transport Flow Matching (OTFM) framework, which integrates the dual formulation of unbalanced optimal transport (UOT) to achieve one-step, high-quality pansharpening. Unlike conventional OT formulations that enforce rigid distribution alignment, UOT relaxes marginal constraints to enhance modeling flexibility, accommodating the intrinsic spectral and spatial disparities in remote sensing data. Furthermore, we incorporate task-specific regularization into the UOT objective, enhancing the robustness of the flow model. The OTFM framework enables simulation-free training and single-step inference while maintaining strict adherence to pansharpening constraints. Experimental evaluations across multiple datasets demonstrate that OTFM matches or exceeds the performance of previous regression-based models and leading diffusion-based methods while only needing one sampling step. Codes are available at https://github.com/294coder/PAN-OTFM.