# Structured Diffusion Models with Mixture of Gaussians as Prior Distribution arXiv: https://arxiv.org/abs/2410.19149 ยท HTML: https://mlsanity.com/paper/2410.19149/ ## Key facts - Cited by 9 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 43 of its 56 references that are in the map. - First posted on arXiv 24 Oct 2024. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 43) - [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) - [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) - [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023) - [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021) - [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020) - [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022) - [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022) - [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021) - [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022) - [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021) - [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022) - [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023) - [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022) - [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022) - [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022) - [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022) - [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023) - [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023) - [SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2309.05019/) (2023) - [Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial](https://mlsanity.com/paper/2402.07487/) (2024) ## Built on by (most cited first, 9 of 9) - [Efficient Flow Matching using Latent Variables](https://mlsanity.com/paper/2505.04486/) (2025) - [Toward Theoretical Insights into Diffusion Trajectory Distillation via Operator Merging](https://mlsanity.com/paper/2505.16024/) (2025) - [Block Flow: Learning Straight Flow on Data Blocks](https://mlsanity.com/paper/2501.11361/) (2025) - [Residual Prior Diffusion: A Probabilistic Framework Integrating Coarse Latent Priors with Diffusion Models](https://mlsanity.com/paper/2512.21593/) (2025) - [DADP: Domain Adaptive Diffusion Policy](https://mlsanity.com/paper/2602.04037/) (2026) - [A Quantitative Approximation Framework for Flow Distillation in Diffusion Models](https://mlsanity.com/paper/2606.03820/) (2026) - [Spatially-Grounded Flow Matching: Structured Source Distributions for Image Generation](https://mlsanity.com/paper/2608.15452/) (2026) - [Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectories](https://mlsanity.com/paper/2609.22867/) (2026) - [Guidance Without Labels: Flow Matching from Coupled Gaussian Mixtures](https://mlsanity.com/paper/2610.16654/) (2026) ## Abstract (arXiv) We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to incorporate certain structured information of the data. We develop a simple-to-implement training procedure that smoothly accommodates the use of mixed Gaussian as prior. Theory is provided to quantify the benefits of our proposed models, compared to the classical diffusion models. Numerical experiments with synthetic, image and operational data are conducted to show comparative advantages of our model. Our method is shown to be robust to mis-specifications and in particular suits situations where training resources are limited or faster training in real time is desired.