Residualized Temporal Sparse Autoencoders for Interpreting Diffusion Models

Abstract

Text-to-image diffusion models generate images by iterative denoising, so their internal layers produce trajectories of activations rather than single static representations. Sparse autoencoders (SAEs) have recently been used to decompose diffusion activations into interpretable features, but most approaches analyze individual timesteps or condition on time rather than learning from full trajectories. Training one SAE on whole trajectories would make each feature a single trajectory across timesteps, but adjacent activations are largely linearly predictable from one another, so such an SAE spends its latents on content carried forward from step to step. We introduce residualized temporal SAEs (ReSAE), which fit linear predictors between neighboring timesteps and represent each trajectory by its initial activation and the residuals these dynamics leave unexplained. Training an SAE on this representation is equivalent to training it on raw trajectories under a metric induced by the linear dynamics, and it encourages latents to capture structure beyond what is linearly predictable. Each latent's decoder direction maps back to activation space as a feature trajectory over denoising time. Across Stable Diffusion~1.5 and a Diffusion Transformer, ReSAE features span the whole trajectory while pinpointing when changes enter it, making ReSAE a natural tool for studying how a diffusion model generates an image over time.