# Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptation

arXiv: https://arxiv.org/abs/2602.20479 · HTML: https://mlsanity.com/paper/2602.20479/

## 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 54 of its 67 references that are in the map.
- First posted on arXiv 24 Feb 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 54)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Conditional Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2203.05557/) (2022)
- [Grounded Language-Image Pre-training](https://mlsanity.com/paper/2112.03857/) (2021)
- [CLIP-Adapter: Better Vision-Language Models with Feature Adapters](https://mlsanity.com/paper/2110.04544/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [RegionCLIP: Region-based Language-Image Pretraining](https://mlsanity.com/paper/2112.09106/) (2021)
- [Tip-Adapter: Training-free Adaption of CLIP for Few-shot Classification](https://mlsanity.com/paper/2207.09519/) (2022)
- [Prompt-aligned Gradient for Prompt Tuning](https://mlsanity.com/paper/2205.14865/) (2022)
- [Visual-Language Prompt Tuning with Knowledge-guided Context Optimization](https://mlsanity.com/paper/2303.13283/) (2023)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [PPT: Pre-trained Prompt Tuning for Few-shot Learning](https://mlsanity.com/paper/2109.04332/) (2021)

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

- [FlowComposer: Composable Flows for Compositional Zero-Shot Learning](https://mlsanity.com/paper/2603.16641/) (2026)
- [FlowCIR: Semantic Transport via Flow Matching for Zero-Shot Composed Image Retrieval](https://mlsanity.com/paper/2607.02284/) (2026)
- [FlowMotion: Training-Free Flow Guidance for Video Motion Transfer](https://mlsanity.com/paper/2603.06289/) (2026)
- [Direct Product Flow Matching: Decoupling Radial and Angular Dynamics for Few-Shot Adaptation](https://mlsanity.com/paper/2605.05054/) (2026)

## Abstract (arXiv)

Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat geometry, where polynomial volume growth fails to accommodate diverse feature distributions, leading to severe path entanglement. To this end, we propose path-decoupled Hyperbolic Flow Matching (HFM), leveraging the Lorentz manifold's exponential expansion for trajectory decoupling. HFM structures the transport via two key designs: 1) Centripetal hyperbolic alignment: It constructs a centripetal hierarchy by anchoring textual roots, which pushes visual leaves to the boundary to initialize orderly flows. 2) Path-decoupled objective: It acts as a ``semantic guardrail'' rigidly confining trajectories within isolated class-specific geodesic corridors via step-wise supervision. Furthermore, we devise an adaptive diameter-based stopping to prevent over-transportation into the crowded origin based on the intrinsic semantic scale. Extensive ablations on 11 benchmarks have shown that HFM establishes a new state-of-the-art, consistently outperforming its Euclidean counterparts. Our codes and models will be released.