# Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders

arXiv: https://arxiv.org/abs/2202.09671 · HTML: https://mlsanity.com/paper/2202.09671/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 71 of its 101 references that are in the map.
- First posted on arXiv 19 Feb 2022.

## Placed in

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

## Builds on (most cited first, 30 of 71)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)

## Built on by (most cited first, 30 of 42)

- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [ModelScope Text-to-Video Technical Report](https://mlsanity.com/paper/2308.06571/) (2023)
- [I2VGen-XL: High-Quality Image-to-Video Synthesis via Cascaded Diffusion Models](https://mlsanity.com/paper/2311.04145/) (2023)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPT](https://mlsanity.com/paper/2303.04226/) (2023)
- [Diffusion-GAN: Training GANs with Diffusion](https://mlsanity.com/paper/2206.02262/) (2022)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Accelerating Diffusion Models via Early Stop of the Diffusion Process](https://mlsanity.com/paper/2205.12524/) (2022)
- [Align Your Steps: Optimizing Sampling Schedules in Diffusion Models](https://mlsanity.com/paper/2404.14507/) (2024)
- [TFMQ-DM: Temporal Feature Maintenance Quantization for Diffusion Models](https://mlsanity.com/paper/2311.16503/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Conditional Simulation Using Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2202.13460/) (2022)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [Adversarial Score identity Distillation: Rapidly Surpassing the Teacher in One Step](https://mlsanity.com/paper/2410.14919/) (2024)
- [Efficient Diffusion Models: A Comprehensive Survey from Principles to Practices](https://mlsanity.com/paper/2410.11795/) (2024)
- [Foundation Models for Music: A Survey](https://mlsanity.com/paper/2408.14340/) (2024)
- [How Much is Enough? A Study on Diffusion Times in Score-based Generative Models](https://mlsanity.com/paper/2206.05173/) (2022)
- [Multi-Architecture Multi-Expert Diffusion Models](https://mlsanity.com/paper/2306.04990/) (2023)
- [ResGrad: Residual Denoising Diffusion Probabilistic Models for Text to Speech](https://mlsanity.com/paper/2212.14518/) (2022)
- [Optimizing Diffusion Models for Joint Trajectory Prediction and Controllable Generation](https://mlsanity.com/paper/2408.00766/) (2024)
- [Ditto: Accelerating Diffusion Model via Temporal Value Similarity](https://mlsanity.com/paper/2501.11211/) (2025)
- [Few-Step Diffusion via Score identity Distillation](https://mlsanity.com/paper/2505.12674/) (2025)
- [Fast Inference in Denoising Diffusion Models via MMD Finetuning](https://mlsanity.com/paper/2301.07969/) (2023)
- [Score Distillation of Flow Matching Models](https://mlsanity.com/paper/2509.25127/) (2025)
- [Multi-scale Latent Point Consistency Models for 3D Shape Generation](https://mlsanity.com/paper/2412.19413/) (2024)

## Abstract (arXiv)

Employing a forward diffusion chain to gradually map the data to a noise distribution, diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. However, this approach is slow and costly because it needs many forward and reverse steps. We propose a faster and cheaper approach that adds noise not until the data become pure random noise, but until they reach a hidden noisy data distribution that we can confidently learn. Then, we use fewer reverse steps to generate data by starting from this hidden distribution that is made similar to the noisy data. We reveal that the proposed model can be cast as an adversarial auto-encoder empowered by both the diffusion process and a learnable implicit prior. Experimental results show even with a significantly smaller number of reverse diffusion steps, the proposed truncated diffusion probabilistic models can provide consistent improvements over the non-truncated ones in terms of performance in both unconditional and text-guided image generations.