Spectrum Matching: a Unified Perspective for Superior Diffusability in Latent Diffusion
This work addresses the challenge of optimizing latent representations for diffusion models, which is important for researchers and practitioners in generative AI, though it appears incremental as it builds on and unifies existing observations and methods.
The paper tackles the problem of improving the learnability (diffusability) of variational autoencoders in latent diffusion by showing that pixel-space diffusion is biased toward low and mid frequencies, which is beneficial due to natural image statistics. It proposes the Spectrum Matching Hypothesis, which requires latents to have a flattened power-law power spectral density and preserve frequency semantics, leading to superior diffusion generation on CelebA and ImageNet datasets, outperforming prior methods.
In this paper, we study the diffusability (learnability) of variational autoencoders (VAE) in latent diffusion. First, we show that pixel-space diffusion trained with an MSE objective is inherently biased toward learning low and mid spatial frequencies, and that the power-law power spectral density (PSD) of natural images makes this bias perceptually beneficial. Motivated by this result, we propose the \emph{Spectrum Matching Hypothesis}: latents with superior diffusability should (i) follow a flattened power-law PSD (\emph{Encoding Spectrum Matching}, ESM) and (ii) preserve frequency-to-frequency semantic correspondence through the decoder (\emph{Decoding Spectrum Matching}, DSM). In practice, we apply ESM by matching the PSD between images and latents, and DSM via shared spectral masking with frequency-aligned reconstruction. Importantly, Spectrum Matching provides a unified view that clarifies prior observations of over-noisy or over-smoothed latents, and interprets several recent methods as special cases (e.g., VA-VAE, EQ-VAE). Experiments suggest that Spectrum Matching yields superior diffusion generation on CelebA and ImageNet datasets, and outperforms prior approaches. Finally, we extend the spectral view to representation alignment (REPA): we show that the directional spectral energy of the target representation is crucial for REPA, and propose a DoG-based method to further improve the performance of REPA. Our code is available https://github.com/forever208/SpectrumMatching.