# Isometric Representation Learning for Disentangled Latent Space of Diffusion Models

arXiv: https://arxiv.org/abs/2407.11451 · HTML: https://mlsanity.com/paper/2407.11451/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 38 of its 62 references that are in the map.
- First posted on arXiv 16 Jul 2024.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [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)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [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)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)

## Built on by (most cited first, 22 of 22)

- [SAeUron: Interpretable Concept Unlearning in Diffusion Models with Sparse Autoencoders](https://mlsanity.com/paper/2501.18052/) (2025)
- [TIDE : Temporal-Aware Sparse Autoencoders for Interpretable Diffusion Transformers in Image Generation](https://mlsanity.com/paper/2503.07050/) (2025)
- [Latent Diffusion Models with Masked AutoEncoders](https://mlsanity.com/paper/2507.09984/) (2025)
- [SAEmnesia: Erasing Concepts in Diffusion Models with Supervised Sparse Autoencoders](https://mlsanity.com/paper/2509.21379/) (2025)
- [Latent Wavelet Diffusion For Ultra-High-Resolution Image Synthesis](https://mlsanity.com/paper/2506.00433/) (2025)
- [Is There a Better Source Distribution than Gaussian? Exploring Source Distributions for Image Flow Matching](https://mlsanity.com/paper/2512.18184/) (2025)
- [SummDiff: Generative Modeling of Video Summarization with Diffusion](https://mlsanity.com/paper/2510.08458/) (2025)
- [Latent Space Disentanglement in Diffusion Transformers Enables Precise Zero-shot Semantic Editing](https://mlsanity.com/paper/2411.08196/) (2024)
- [Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models](https://mlsanity.com/paper/2510.05509/) (2025)
- [CLAD: Constrained Latent Action Diffusion for Vision-Language Procedure Planning](https://mlsanity.com/paper/2503.06637/) (2025)
- [Contrastive Diffusion Alignment: Learning Structured Latents for Controllable Generation](https://mlsanity.com/paper/2510.14190/) (2025)
- [Latent Space Disentanglement in Diffusion Transformers Enables Zero-shot Fine-grained Semantic Editing](https://mlsanity.com/paper/2408.13335/) (2024)
- [SC-Pro: Training-Free Framework for Defending Unsafe Image Synthesis Attack](https://mlsanity.com/paper/2501.05359/) (2025)
- [SPF-Portrait: Towards Pure Text-to-Portrait Customization with Semantic Pollution-Free Fine-Tuning](https://mlsanity.com/paper/2504.00396/) (2025)
- [Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularization](https://mlsanity.com/paper/2505.04412/) (2025)
- [Discovering Data Manifold Geometry through Geometric Properties](https://mlsanity.com/paper/2602.02611/) (2026)
- [Expressive Score-Based Priors for Distribution Matching with Geometry-Preserving Regularization](https://mlsanity.com/paper/2506.14607/) (2025)
- [Style Composition within Distinct LoRA modules for Traditional Art](https://mlsanity.com/paper/2507.11986/) (2025)
- [FLUID: Training-Free Face De-identification via Latent Identity Substitution](https://mlsanity.com/paper/2511.17005/) (2025)
- [Equivariant Latent Alignment via Flow Matching under Group Symmetries](https://mlsanity.com/paper/2605.30705/) (2026)
- [From Noise to Control: Parameterized Diffusion Policies](https://mlsanity.com/paper/2606.00336/) (2026)
- [Interpreting Object-Dependent Concept Brittleness in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2609.09909/) (2026)

## Abstract (arXiv)

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping from its latent space to image space. To tackle this problem, we present Isometric Diffusion, equipping a diffusion model with a geometric regularizer to guide the model to learn a geometrically sound latent space of the training data manifold. This approach allows diffusion models to learn a more disentangled latent space, which enables smoother interpolation, more accurate inversion, and more precise control over attributes directly in the latent space. Our extensive experiments consisting of image interpolations, image inversions, and linear editing show the effectiveness of our method.