mlsanityData to 7 Oct 2026

Understanding Latent Diffusability via Fisher Geometry

arXiv 2604.02751 ↗First posted 3 Apr 2026cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

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.

Key facts. No citing papers in the map yet (data through 7 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.

Builds on

30 of 46 references.

Closest ancestors · 18

Same direction, newest first

  1. 2026Unified Latents (UL): How to train your latents19 Feb
  2. 2026Image Generation with a Sphere Encoder16 Feb
  3. 2026Latent Forcing: Reordering the Diffusion Trajectory for Pixel-Space Image Generation11 Feb
  4. 2025Latent Diffusion Model without Variational Autoencoder17 Oct
  5. 2025Diffusion Transformers with Representation Autoencoders13 Oct
  6. 2025Latent Diffusion Models with Masked AutoEncoders14 Jul
  7. 2025Hessian Geometry of Latent Space in Generative Models12 Jun
  8. 2025The Spacetime of Diffusion Models: An Information Geometry Perspective23 May
  9. 2025Enhancing Variational Autoencoders with Smooth Robust Latent Encoding24 Apr
  10. 2025REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers14 Apr
  11. 2025Improving the Diffusability of Autoencoders20 Feb
  12. 2025Geometry-Preserving Encoder/Decoder in Latent Generative Models16 Jan
6 more
  1. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers16 Jan
  2. 2022Scalable Diffusion Models with Transformers19 Dec
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 12

  1. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  2. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  3. 2018On the Spectral Bias of Neural Networkscited by 1,321
  4. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  5. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 360
  6. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 307
  7. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 169
  8. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 85
  9. 2020Learning Flat Latent Manifolds with VAEscited by 33
  10. 2023Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimizationcited by 18
  11. 2022Hyperbolic VAE via Latent Gaussian Distributionscited by 14
  12. 2025Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolationcited by 5

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry
  2. 2026Diffusing in the Right Space: A Systematic Study of Latent Diffusability
  3. 2025Optimal Stopping in Latent Diffusion Models
  4. 2026On the Limits of Latent Reuse in Diffusion Models
  5. 2026When Diffusion Model Can Ignore Dimension: An Entropy-Based Theory
  6. 2025Latent Diffusion Inversion Requires Understanding the Latent Space
  7. 2026Evaluating the Representation Space of Diffusion Models via Self-Supervised Principles
  8. 2026Intrinsic-Hybrid Latent Diffusion Models for Generative Modeling on Unknown Manifolds