# Understanding Latent Diffusability via Fisher Geometry

arXiv: https://arxiv.org/abs/2604.02751 · HTML: https://mlsanity.com/paper/2604.02751/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Placed in

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

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

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers](https://mlsanity.com/paper/2504.10483/) (2025)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modeling](https://mlsanity.com/paper/2502.09509/) (2025)
- [Latent Diffusion Model without Variational Autoencoder](https://mlsanity.com/paper/2510.15301/) (2025)
- [Improving the Diffusability of Autoencoders](https://mlsanity.com/paper/2502.14831/) (2025)
- [Latent Forcing: Reordering the Diffusion Trajectory for Pixel-Space Image Generation](https://mlsanity.com/paper/2602.11401/) (2026)
- [Learning Flat Latent Manifolds with VAEs](https://mlsanity.com/paper/2002.04881/) (2020)
- [Unified Latents (UL): How to train your latents](https://mlsanity.com/paper/2602.17270/) (2026)
- [Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimization](https://mlsanity.com/paper/2309.04810/) (2023)
- [Hyperbolic VAE via Latent Gaussian Distributions](https://mlsanity.com/paper/2209.15217/) (2022)
- [Latent Diffusion Models with Masked AutoEncoders](https://mlsanity.com/paper/2507.09984/) (2025)
- [Hessian Geometry of Latent Space in Generative Models](https://mlsanity.com/paper/2506.10632/) (2025)
- [Image Generation with a Sphere Encoder](https://mlsanity.com/paper/2602.15030/) (2026)
- [Geometry-Preserving Encoder/Decoder in Latent Generative Models](https://mlsanity.com/paper/2501.09876/) (2025)
- [Enhancing Variational Autoencoders with Smooth Robust Latent Encoding](https://mlsanity.com/paper/2504.17219/) (2025)
- [The Spacetime of Diffusion Models: An Information Geometry Perspective](https://mlsanity.com/paper/2505.17517/) (2025)
- [Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation](https://mlsanity.com/paper/2507.11789/) (2025)

## Abstract (arXiv)

Diffusion models often degrade in latent spaces, yet the formal causes remain poorly understood. We quantify latent-space diffusability via the rate of change of the Minimum Mean Squared Error (MMSE) along the diffusion trajectory. Our framework decomposes this MMSE rate into contributions from Fisher Information (FI) and Fisher Information Rate (FIR). We show that isometric embeddings preserve intrinsic FI and establish quantitative intrinsic-FI bounds for a broader class of bi-Lipschitz encoders with controlled weak volume distortion, whereas FIR is governed by the interplay between encoder and data geometries. Our analysis separates four geometric contributions in local stability bounds for Gaussian-smoothed FIR: dimensional compression, tangential distortion, high-frequency encoder curvature, and curvature of data manifold. Experiments across diverse autoencoding architectures provide qualitative support for the geometric mechanisms identified by the theory and show that empirical FI and FIR track several measures of generation quality and latent-space geometry in the settings tested. We establish FI and FIR as a comprehensive analytical framework for understanding latent diffusability.