Spectrum Matching: a Unified Perspective for Superior Diffusability in Latent Diffusion
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 Spectrum Matching Hypothesis: latents with superior diffusability should (i) follow a flattened power-law PSD (Encoding Spectrum Matching, ESM) and (ii) preserve frequency-to-frequency semantic correspondence through the decoder (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.
69b97d0eebc57f8925831f41
Mang Ning
69b97d0eebc57f8925831f42
Mingxiao Li
69b97d0eebc57f8925831f43
Le Zhang
69b97d0eebc57f8925831f44
Lanmiao Liu
69b97d0eebc57f8925831f45
Matthew B. Blaschko
69b97d0eebc57f8925831f46
Albert Ali Salah
69b97d0eebc57f8925831f47
Itir Onal Ertugrul
Spectrum Matching: a Unified Perspective for Superior Diffusability in Latent Diffusion
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 Spectrum Matching Hypothesis: latents with superior diffusability should (i) follow a flattened power-law PSD (Encoding Spectrum Matching, ESM) and (ii) preserve frequency-to-frequency semantic correspondence through the decoder (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.
Variational autoencoders' learnability in latent diffusion is enhanced through spectrum matching techniques that align power-law spectral densities and preserve frequency semantics during encoding and decoding processes.
variational autoencoders latent diffusion power-law power spectral density spectrum matching hypothesis encoding spectrum matching decoding spectrum matching spectral masking frequency-aligned reconstruction representation alignment directional spectral energy DoG-based method