# Residualized Temporal Sparse Autoencoders for Interpreting Diffusion Models

arXiv: https://arxiv.org/abs/2605.27813 · HTML: https://mlsanity.com/paper/2605.27813/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 26 of its 30 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)
- Mechanistic interpretability / [Interpreting and steering diffusion models](https://mlsanity.com/mechinterp/interpreting-and-steering-diffusion-models/)

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Grounded SAM: Assembling Open-World Models for Diverse Visual Tasks](https://mlsanity.com/paper/2401.14159/) (2024)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Label-Efficient Semantic Segmentation with Diffusion Models](https://mlsanity.com/paper/2112.03126/) (2021)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [Diffusion Self-Guidance for Controllable Image Generation](https://mlsanity.com/paper/2306.00986/) (2023)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence](https://mlsanity.com/paper/2305.15347/) (2023)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [What the DAAM: Interpreting Stable Diffusion Using Cross Attention](https://mlsanity.com/paper/2210.04885/) (2022)
- [Diffusion Hyperfeatures: Searching Through Time and Space for Semantic Correspondence](https://mlsanity.com/paper/2305.14334/) (2023)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [SAeUron: Interpretable Concept Unlearning in Diffusion Models with Sparse Autoencoders](https://mlsanity.com/paper/2501.18052/) (2025)
- [One-Step is Enough: Sparse Autoencoders for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2410.22366/) (2024)
- [Emergence and Evolution of Interpretable Concepts in Diffusion Models](https://mlsanity.com/paper/2504.15473/) (2025)
- [Temporal Sparse Autoencoders: Leveraging the Sequential Nature of Language for Interpretability](https://mlsanity.com/paper/2511.05541/) (2025)
- [TIDE : Temporal-Aware Sparse Autoencoders for Interpretable Diffusion Transformers in Image Generation](https://mlsanity.com/paper/2503.07050/) (2025)
- [Concept Steerers: Leveraging K-Sparse Autoencoders for Test-Time Controllable Generations](https://mlsanity.com/paper/2501.19066/) (2025)
- [Interpreting Large Text-to-Image Diffusion Models with Dictionary Learning](https://mlsanity.com/paper/2505.24360/) (2025)

## Built on by (most cited first, 1 of 1)

- [D-Scope: Decomposing and Steering Diffusion Transformers with Sparse Autoencoders](https://mlsanity.com/paper/2609.39625/) (2026)

## Abstract (arXiv)

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.