# Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models

arXiv: https://arxiv.org/abs/2303.11073 · HTML: https://mlsanity.com/paper/2303.11073/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 42 of its 48 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 42)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Closed-Form Factorization of Latent Semantics in GANs](https://mlsanity.com/paper/2007.06600/) (2020)
- [InterFaceGAN: Interpreting the Disentangled Face Representation Learned by GANs](https://mlsanity.com/paper/2005.09635/) (2020)
- [Image2StyleGAN++: How to Edit the Embedded Images?](https://mlsanity.com/paper/1911.11544/) (2019)

## Built on by (most cited first, 30 of 60)

- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Concept Sliders: LoRA Adaptors for Precise Control in Diffusion Models](https://mlsanity.com/paper/2311.12092/) (2023)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [A Neural Space-Time Representation for Text-to-Image Personalization](https://mlsanity.com/paper/2305.15391/) (2023)
- [Self-Discovering Interpretable Diffusion Latent Directions for Responsible Text-to-Image Generation](https://mlsanity.com/paper/2311.17216/) (2023)
- [LooseControl: Lifting ControlNet for Generalized Depth Conditioning](https://mlsanity.com/paper/2312.03079/) (2023)
- [Zero-Shot Unsupervised and Text-Based Audio Editing Using DDPM Inversion](https://mlsanity.com/paper/2402.10009/) (2024)
- [NoiseCLR: A Contrastive Learning Approach for Unsupervised Discovery of Interpretable Directions in Diffusion Models](https://mlsanity.com/paper/2312.05390/) (2023)
- [Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Space](https://mlsanity.com/paper/2406.19370/) (2024)
- [Latent Space Editing in Transformer-Based Flow Matching](https://mlsanity.com/paper/2312.10825/) (2023)
- [Emergence and Evolution of Interpretable Concepts in Diffusion Models](https://mlsanity.com/paper/2504.15473/) (2025)
- [DiffusionPID: Interpreting Diffusion via Partial Information Decomposition](https://mlsanity.com/paper/2406.05191/) (2024)
- [Global Counterfactual Directions](https://mlsanity.com/paper/2404.12488/) (2024)
- [FouRA: Fourier Low Rank Adaptation](https://mlsanity.com/paper/2406.08798/) (2024)
- [Exploring Low-Dimensional Subspaces in Diffusion Models for Controllable Image Editing](https://mlsanity.com/paper/2409.02374/) (2024)
- [Uncovering the Text Embedding in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2404.01154/) (2024)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [Probing the Representational Power of Sparse Autoencoders in Vision Models](https://mlsanity.com/paper/2508.11277/) (2025)
- [Linear combinations of latents in generative models: subspaces and beyond](https://mlsanity.com/paper/2408.08558/) (2024)
- [Diffusion Generative Modeling on Lie Group Representations](https://mlsanity.com/paper/2502.02513/) (2025)
- [Training-Free Style and Content Transfer by Leveraging U-Net Skip Connections in Stable Diffusion](https://mlsanity.com/paper/2501.14524/) (2025)
- [An Analysis of Human Alignment of Latent Diffusion Models](https://mlsanity.com/paper/2403.08469/) (2024)
- [Plug-and-Play Interpretable Responsible Text-to-Image Generation via Dual-Space Multi-facet Concept Control](https://mlsanity.com/paper/2503.18324/) (2025)
- [Spanning the Visual Analogy Space with a Weight Basis of LoRAs](https://mlsanity.com/paper/2602.15727/) (2026)
- [Latent Abstractions in Generative Diffusion Models](https://mlsanity.com/paper/2410.03368/) (2024)
- [UniLight: A Unified Representation for Lighting](https://mlsanity.com/paper/2512.04267/) (2025)
- [On the Semantic Latent Space of Diffusion-Based Text-to-Speech Models](https://mlsanity.com/paper/2402.12423/) (2024)
- [Exploring the Potentials and Challenges of Deep Generative Models in Product Design Conception](https://mlsanity.com/paper/2407.11104/) (2024)
- [Enabling Local Editing in Diffusion Models by Joint and Individual Component Analysis](https://mlsanity.com/paper/2408.16845/) (2024)
- [Preference Alignment for Diffusion Model via Explicit Denoised Distribution Estimation](https://mlsanity.com/paper/2411.14871/) (2024)

## Abstract (arXiv)

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.