# Iterative α-(de)Blending: a Minimalist Deterministic Diffusion Model

arXiv: https://arxiv.org/abs/2305.03486 · HTML: https://mlsanity.com/paper/2305.03486/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 5 May 2023.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [Denoising Diffusion Gamma Models](https://mlsanity.com/paper/2110.05948/) (2021)
- [Heavy-tailed denoising score matching](https://mlsanity.com/paper/2112.09788/) (2021)

## Built on by (most cited first, 30 of 46)

- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Error Bounds for Flow Matching Methods](https://mlsanity.com/paper/2305.16860/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies](https://mlsanity.com/paper/2402.04292/) (2024)
- [Closed-Form Diffusion Models](https://mlsanity.com/paper/2310.12395/) (2023)
- [Exploiting Diffusion Prior for Generalizable Dense Prediction](https://mlsanity.com/paper/2311.18832/) (2023)
- [Much Ado About Noising: Dispelling the Myths of Generative Robotic Control](https://mlsanity.com/paper/2512.01809/) (2025)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)
- [Flowing from Words to Pixels: A Noise-Free Framework for Cross-Modality Evolution](https://mlsanity.com/paper/2412.15213/) (2024)
- [Augmented Bridge Matching](https://mlsanity.com/paper/2311.06978/) (2023)
- [SemFlow: Binding Semantic Segmentation and Image Synthesis via Rectified Flow](https://mlsanity.com/paper/2405.20282/) (2024)
- [Stochastic Sampling from Deterministic Flow Models](https://mlsanity.com/paper/2410.02217/) (2024)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [AMO Sampler: Enhancing Text Rendering with Overshooting](https://mlsanity.com/paper/2411.19415/) (2024)
- [Neodragon: Mobile Video Generation using Diffusion Transformer](https://mlsanity.com/paper/2511.06055/) (2025)
- [Video Latent Flow Matching: Optimal Polynomial Projections for Video Interpolation and Extrapolation](https://mlsanity.com/paper/2502.00500/) (2025)
- [Statistical Properties of Rectified Flow](https://mlsanity.com/paper/2511.03193/) (2025)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows](https://mlsanity.com/paper/2503.09069/) (2025)
- [EVODiff: Entropy-aware Variance Optimized Diffusion Inference](https://mlsanity.com/paper/2509.26096/) (2025)
- [Improving Rectified Flow with Boundary Conditions](https://mlsanity.com/paper/2506.15864/) (2025)
- [AdBooster: Personalized Ad Creative Generation using Stable Diffusion Outpainting](https://mlsanity.com/paper/2309.11507/) (2023)
- [Local Diffusion Models and Phases of Data Distributions](https://mlsanity.com/paper/2508.06614/) (2025)
- [Finite Difference Flow Optimization for RL Post-Training of Text-to-Image Models](https://mlsanity.com/paper/2603.12893/) (2026)
- [Unsupervised Composable Representations for Audio](https://mlsanity.com/paper/2408.09792/) (2024)
- [Geometric Regularity in Deterministic Sampling Dynamics of Diffusion-based Generative Models](https://mlsanity.com/paper/2506.10177/) (2025)
- [Generative Video Bi-flow](https://mlsanity.com/paper/2503.06364/) (2025)
- [Aligning Latent Spaces with Flow Priors](https://mlsanity.com/paper/2506.05240/) (2025)

## Abstract (arXiv)

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.