# Dimensionality-Varying Diffusion Process arXiv: https://arxiv.org/abs/2211.16032 · HTML: https://mlsanity.com/paper/2211.16032/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 29 of its 34 references that are in the map. - First posted on arXiv 29 Nov 2022. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 29 of 29) - [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) - [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) - [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (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) - [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018) - [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021) - [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015) - [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021) - [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022) - [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021) - [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021) - [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022) - [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022) - [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021) - [ImageBART: Bidirectional Context with Multinomial Diffusion for Autoregressive Image Synthesis](https://mlsanity.com/paper/2108.08827/) (2021) - [Noise Estimation for Generative Diffusion Models](https://mlsanity.com/paper/2104.02600/) (2021) - [Diffusion Normalizing Flow](https://mlsanity.com/paper/2110.07579/) (2021) - [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022) - [Global Context with Discrete Diffusion in Vector Quantised Modelling for Image Generation](https://mlsanity.com/paper/2112.01799/) (2021) - [Progressive Deblurring of Diffusion Models for Coarse-to-Fine Image Synthesis](https://mlsanity.com/paper/2207.11192/) (2022) - [Pyramidal Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2208.01864/) (2022) - [Improving Diffusion Model Efficiency Through Patching](https://mlsanity.com/paper/2207.04316/) (2022) ## Built on by (most cited first, 12 of 12) - [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024) - [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024) - [Trans-Dimensional Generative Modeling via Jump Diffusion Models](https://mlsanity.com/paper/2305.16261/) (2023) - [Idempotence and Perceptual Image Compression](https://mlsanity.com/paper/2401.08920/) (2024) - [∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States](https://mlsanity.com/paper/2303.18242/) (2023) - [Lipschitz Singularities in Diffusion Models](https://mlsanity.com/paper/2306.11251/) (2023) - [Just-in-Time: Training-Free Spatial Acceleration for Diffusion Transformers](https://mlsanity.com/paper/2603.10744/) (2026) - [Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction](https://mlsanity.com/paper/2411.03758/) (2024) - [Towards Redundancy Reduction in Diffusion Models for Efficient Video Super-Resolution](https://mlsanity.com/paper/2509.23980/) (2025) - [Image Restoration via Diffusion Models with Dynamic Resolution](https://mlsanity.com/paper/2605.14267/) (2026) - [Conditional Diffusion Model for Electrical Impedance Tomography](https://mlsanity.com/paper/2501.05769/) (2025) - [Generate the Forest before the Trees -- A Hierarchical Diffusion model for Climate Downscaling](https://mlsanity.com/paper/2506.19391/) (2025) ## Abstract (arXiv) Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at 1024×1024 resolution from 52.40 to 10.46. Code and models will be made publicly available.