# Symmetrical Flow Matching: Unified Image Generation, Segmentation, and Classification with Score-Based Generative Models

arXiv: https://arxiv.org/abs/2506.10634 · HTML: https://mlsanity.com/paper/2506.10634/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 47 of its 64 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## 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, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs](https://mlsanity.com/paper/1711.11585/) (2017)
- [Per-Pixel Classification is Not All You Need for Semantic Segmentation](https://mlsanity.com/paper/2107.06278/) (2021)
- [COCO-Stuff: Thing and Stuff Classes in Context](https://mlsanity.com/paper/1612.03716/) (2016)
- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Label-Efficient Semantic Segmentation with Diffusion Models](https://mlsanity.com/paper/2112.03126/) (2021)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [SegDiff: Image Segmentation with Diffusion Probabilistic Models](https://mlsanity.com/paper/2112.00390/) (2021)
- [SEAN: Image Synthesis with Semantic Region-Adaptive Normalization](https://mlsanity.com/paper/1911.12861/) (2019)

## Built on by (most cited first, 8 of 8)

- [MedSymmFlow: Bridging Generative Modeling and Classification in Medical Imaging through Symmetrical Flow Matching](https://mlsanity.com/paper/2507.19098/) (2025)
- [Preconditioned Flow Matching](https://mlsanity.com/paper/2603.02337/) (2026)
- [Rethinking Vector Field Learning for Generative Segmentation](https://mlsanity.com/paper/2603.19218/) (2026)
- [Joint Flow Matching for Generator-Consistent Classification](https://mlsanity.com/paper/2607.23946/) (2026)
- [Representation-driven Endoscopic Visual Embedding Alignment for Latent Generation](https://mlsanity.com/paper/2608.07176/) (2026)
- [SymmAdapt: Symmetrical Flow Matching for Source-Free Domain Adaptation in Medical Image Segmentation](https://mlsanity.com/paper/2608.22532/) (2026)
- [Representation Learning in Diffusion and Flow-based Model: An Application Aspect](https://mlsanity.com/paper/2608.24068/) (2026)
- [Drift Variation Autoencoder: Unifying Generation and Representation Learning through Conditional Posterior Flow Matching](https://mlsanity.com/paper/2608.25138/) (2026)

## Abstract (arXiv)

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that unifies semantic segmentation, classification, and image generation within a single model. Using a symmetric learning objective, SymmFlow models forward and reverse transformations jointly, ensuring bi-directional consistency, while preserving sufficient entropy for generative diversity. A new training objective is introduced to explicitly retain semantic information across flows, featuring efficient sampling while preserving semantic structure, allowing for one-step segmentation and classification without iterative refinement. Unlike previous approaches that impose strict one-to-one mapping between masks and images, SymmFlow generalizes to flexible conditioning, supporting both pixel-level and image-level class labels. Experimental results on various benchmarks demonstrate that SymmFlow achieves state-of-the-art performance on semantic image synthesis, obtaining FID scores of 11.9 on CelebAMask-HQ and 7.0 on COCO-Stuff with only 25 inference steps. Additionally, it delivers competitive results on semantic segmentation and shows promising capabilities in classification tasks.