Patch-wise PCA links v-prediction failure to a bandwidth bottleneck
Original title: What kills $v$-prediction? A Patch-wise PCA Perspective on Pixel-Space Flow Matching
A Raw-injected Transformer restores effective v-prediction and is competitive on ImageNet 256×256.
The paper argues that pixel-space flow matching struggles with the standard v-prediction objective because of a bandwidth bottleneck, not only off-manifold noised targets. Patch-wise PCA shows minor-component velocity is largely set by the raw noisy input, so deep backbones must preserve that signal while modeling principal components. The authors say x-prediction works via a raw-input bypass and acts as an implicit conditional-mean decoder under low-rank observations. They introduce the Raw-injected Transformer, combining a lightweight raw-conditioned decoder with an output-side shortcut.
Unconfirmed: Performance claims come from the authors' controlled experiments; independent replication is not reported.
- Analysis covers pixel-space flow matching versus latent diffusion models.
- x-prediction is described as an implicit conditional-mean decoder under low-rank observations.
- RiT separates semantic modeling from raw-state propagation.
- Reported results are on ImageNet 256×256.
From the original article
1 min read at arxiv.orgLatent Diffusion Models dominate generative modeling but face two-stage training complexity and the inherent reconstruction limits of pre-trained autoencoders. Pixel-space Flow Matching offers a simplified end-to-end alternative yet often encounters training difficulties when using the standard $v$-prediction objective.
By Tianze Luo · arxiv.org
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