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About this paper
Junyi Lin, Mengyu Li, Jingxuan Hu, Kejun He, Cheng Meng
Quantile AlignTree Flow Matching (QAT-FM) introduces an efficient, structured coupling method that aligns an empirical data distribution with a continuous Gaussian prior using a hierarchical quantile-aligned tree. This approach generates non-crossing interpolation paths for Flow Matching, effectively reducing local velocity ambiguity and improving sample quality, achieving an FID of 3.26 on CIFAR-10 and 2.68 on CelebA-64x64 while maintaining computational efficiency.
Key insights
- A hierarchical quantile-aligned tree structure can efficiently induce an exact coupling between empirical data and a continuous Gaussian prior that inherently leads to strictly non-crossing linear interpolation paths.
- Quantile matching at each tree split ensures source and data regions carry equal mass ratios, leading to marginal consistency and quantifiable improvements in path separation compared to simpler couplings.
- Decoupling how data and condition coordinates are handled during splits in CQAT enables robust conditional generation by refining conditional groups while preserving the global Gaussian alignment for the data component.
Summary by alphaXiv.
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