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This paper investigates the diffusability of variational autoencoders (VAEs) in latent diffusion models, revealing that pixel-space diffusion is biased towards learning low and mid spatial frequencies due to the power-law power spectral density (PSD) of natural images. They propose the Spectrum Matching Hypothesis, which posits that superior latent diffusability requires flattened power-law PSD (Encoding Spectrum Matching, ESM) and preservation of frequency-to-frequency semantic correspondence through the decoder (Decoding Spectrum Matching, DSM). By applying ESM and DSM, the authors achieve superior diffusion generation on CelebA and ImageNet datasets, outperforming prior approaches, and extend the spectral view to representation alignment (REPA) using a DoG-based method.
Latent diffusion models can be significantly improved by matching the power spectral density between images and latents, unifying previous observations of over-noisy or over-smoothed latents under a single "Spectrum Matching Hypothesis."
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.
