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Main Authors: Humayun, Ahmed Imtiaz, Amara, Ibtihel, Vasconcelos, Cristina, Ramachandran, Deepak, Schumann, Candice, He, Junfeng, Heller, Katherine, Farnadi, Golnoosh, Rostamzadeh, Negar, Havaei, Mohammad
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2408.08307
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author Humayun, Ahmed Imtiaz
Amara, Ibtihel
Vasconcelos, Cristina
Ramachandran, Deepak
Schumann, Candice
He, Junfeng
Heller, Katherine
Farnadi, Golnoosh
Rostamzadeh, Negar
Havaei, Mohammad
author_facet Humayun, Ahmed Imtiaz
Amara, Ibtihel
Vasconcelos, Cristina
Ramachandran, Deepak
Schumann, Candice
He, Junfeng
Heller, Katherine
Farnadi, Golnoosh
Rostamzadeh, Negar
Havaei, Mohammad
contents Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer architectures, generation performance can significantly vary across the learned data manifold. In this paper we study the local geometry of the learned manifold and its relationship to generation outcomes for a wide range of generative models, including DDPM, Diffusion Transformer (DiT), and Stable Diffusion 1.4. Building on the theory of continuous piecewise-linear (CPWL) generators, we characterize the local geometry in terms of three geometric descriptors - scaling ($ψ$), rank ($ν$), and complexity/un-smoothness ($δ$). We provide quantitative and qualitative evidence showing that for a given latent-image pair, the local descriptors are indicative of generation aesthetics, diversity, and memorization by the generative model. Finally, we demonstrate that by training a reward model on the local scaling for Stable Diffusion, we can self-improve both generation aesthetics and diversity using `geometry reward' based guidance during denoising.
format Preprint
id arxiv_https___arxiv_org_abs_2408_08307
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models
Humayun, Ahmed Imtiaz
Amara, Ibtihel
Vasconcelos, Cristina
Ramachandran, Deepak
Schumann, Candice
He, Junfeng
Heller, Katherine
Farnadi, Golnoosh
Rostamzadeh, Negar
Havaei, Mohammad
Machine Learning
Computer Vision and Pattern Recognition
Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer architectures, generation performance can significantly vary across the learned data manifold. In this paper we study the local geometry of the learned manifold and its relationship to generation outcomes for a wide range of generative models, including DDPM, Diffusion Transformer (DiT), and Stable Diffusion 1.4. Building on the theory of continuous piecewise-linear (CPWL) generators, we characterize the local geometry in terms of three geometric descriptors - scaling ($ψ$), rank ($ν$), and complexity/un-smoothness ($δ$). We provide quantitative and qualitative evidence showing that for a given latent-image pair, the local descriptors are indicative of generation aesthetics, diversity, and memorization by the generative model. Finally, we demonstrate that by training a reward model on the local scaling for Stable Diffusion, we can self-improve both generation aesthetics and diversity using `geometry reward' based guidance during denoising.
title What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models
topic Machine Learning
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2408.08307