# DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation

arXiv: https://arxiv.org/abs/2602.00656 · HTML: https://mlsanity.com/paper/2602.00656/

## Key facts

- Cited by 4 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 43 of its 67 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## 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 43)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Progressive Feature Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1811.08585/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [CoCo: A Coupled Contrastive Framework for Unsupervised Domain Adaptive Graph Classification](https://mlsanity.com/paper/2306.04979/) (2023)
- [Structural Re-weighting Improves Graph Domain Adaptation](https://mlsanity.com/paper/2306.03221/) (2023)
- [Adversarial Deep Network Embedding for Cross-network Node Classification](https://mlsanity.com/paper/2002.07366/) (2020)
- [AdaGCN: Adaboosting Graph Convolutional Networks into Deep Models](https://mlsanity.com/paper/1908.05081/) (2019)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Path Neural Networks: Expressive and Accurate Graph Neural Networks](https://mlsanity.com/paper/2306.05955/) (2023)
- [Rethinking Propagation for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2402.05660/) (2024)
- [Semi-supervised Domain Adaptation in Graph Transfer Learning](https://mlsanity.com/paper/2309.10773/) (2023)
- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [Latent Graph Inference using Product Manifolds](https://mlsanity.com/paper/2211.16199/) (2022)
- [Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning](https://mlsanity.com/paper/2401.01232/) (2024)

## Built on by (most cited first, 4 of 4)

- [When Agents Learn to Be You: Benchmarking Privacy Leakage, Impersonation Risk, and Defenses in Persona Skills](https://mlsanity.com/paper/2608.03700/) (2026)
- [DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation](https://mlsanity.com/paper/2604.03154/) (2026)
- [Data-Efficient Agentic Graph Domain Adaptation via Reliability-Aware Prototype Learning](https://mlsanity.com/paper/2609.14045/) (2026)
- [CyFM: Cylindrical Optimal Transport for Few-Step Complex-Valued Flow Matching](https://mlsanity.com/paper/2609.14171/) (2026)

## Abstract (arXiv)

Graph Domain Adaptation (GDA) aims to transfer graph classifiers across domains with both semantic and topological shifts. Existing Euclidean adversarial methods face two challenges: Structural Degeneration, where domain confusion entangles and suppresses label-relevant topology, and Optimization Instability, where minimax training induces oscillatory gradients under large structural shifts. We propose DisRFM, a geometry-aware GDA framework that addresses these challenges with Riemannian representation learning and flow-based transport. DisRFM embeds graph representations on a constant-curvature manifold and expresses them in geodesic polar coordinates. Polar endpoint regularization calibrates topologysensitive radial scales via univariate Wasserstein alignment and preserves scalenormalized class semantics through confidence-filtered angular alignment, with radial magnitude modulating pseudo-label reliability. DisRFM introduces topologyconditioned polar flow matching, which couples class-compatible source and target samples by a normalized polar transport cost and learns a metric-corrected vector field along geodesic interpolants. Theoretical analysis characterizes the structural risk of unconditional domain confusion and relates polar discrepancies and flow error to target risk. Extensive experiments under diverse domain shifts demonstrate that DisRFM consistently outperforms state-of-the-art methods.