Spectrum Matching: a Unified Perspective for Superior Diffusability in Latent Diffusion

TL;DR

This paper introduces Spectrum Matching, a unified spectral perspective for improving latent diffusion models by aligning the frequency spectra of images and latents, leading to enhanced generative performance.

Contribution

It proposes the Spectrum Matching hypothesis, combining Encoding and Decoding Spectrum Matching, to improve latent diffusion by spectral alignment, and extends this view to representation alignment with a new DoG-based method.

Findings

Spectrum Matching improves diffusion quality on CelebA and ImageNet.

Matching spectral properties leads to better latent diffusion performance.

The spectral view clarifies prior methods and guides new improvements.

Abstract

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.