Abstract
Latent diffusion models decode approximately correct latents, making decoder sensitivity to perturbations relevant to image quality. After whitening, forward diffusion corrupts every direction at the same signal-to-noise ratio (SNR), despite unequal decoder sensitivities. We study an invertible linear layer between the encoder and diffusion process that shifts each direction's log-SNR. Its linear minimum mean-square-error (LMMSE) recovery risk has an exact spectral expression for any whitened latent distribution. Under an energy budget and a floor ensuring invertibility, minimizing decoder-sensitivity-weighted LMMSE risk integrated over the diffusion schedule yields a unique optimal allocation. The layer aligns with the decoder's expected pullback metric and equalizes marginal risk reduction across directions, computed by a deterministic spectral solver. At large budgets, the allocation follows a power law in sensitivity whose exponent is determined by the low-SNR tail of the loss weighting: one half for noise prediction and two thirds for data prediction under the cosine schedule, with a crossover on truncated schedules. We instantiate this principle as RB-LDC using Jacobian-based sensitivity estimates. On ImageNet at 256 x 256 resolution with SD-VAE and VA-VAE, trained RB-LDC improves reconstruction from noisy latents over budget-matched isotropic coding in all four metrics and five coding configurations, averaged over 15 SNRs and three pipeline seeds. It reduces average perturbed FID by 17.1 for VA-VAE block-local coding while preserving clean reconstruction. We also report intermediate SNRs where perturbed FID worsens. With a frozen diffusion model, RB-LDC yields lower FID point estimates in all 12 tested combinations of sampling progress and channel SNR under corruption during sampling.
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URL
https://arxiv.org/abs/2611.13955
