# Unified Directly Denoising for Both Variance Preserving and Variance Exploding Diffusion Models

arXiv: https://arxiv.org/abs/2405.21059 · HTML: https://mlsanity.com/paper/2405.21059/

## Key facts

- Cited by 1 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 38 references that are in the map.
- First posted on arXiv 31 May 2024.

## 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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [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)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [Diffusion-Based Voice Conversion with Fast Maximum Likelihood Sampling Scheme](https://mlsanity.com/paper/2109.13821/) (2021)
- [Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models](https://mlsanity.com/paper/2211.17091/) (2022)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)

## Built on by (most cited first, 1 of 1)

- [Tortoise and Hare Guidance: Accelerating Diffusion Model Inference with Multirate Integration](https://mlsanity.com/paper/2511.04117/) (2025)

## Abstract (arXiv)

Previous work has demonstrated that, in the Variance Preserving (VP) scenario, the nascent Directly Denoising Diffusion Models (DDDM) can generate high-quality images in one step while achieving even better performance in multistep sampling. However, the Pseudo-LPIPS loss used in DDDM leads to concerns about the bias in assessment. Here, we propose a unified DDDM (uDDDM) framework that generates images in one-step/multiple steps for both Variance Preserving (VP) and Variance Exploding (VE) cases. We provide theoretical proofs of the existence and uniqueness of the model's solution paths, as well as the non-intersecting property of the sampling paths. Additionally, we propose an adaptive Pseudo-Huber loss function to balance the convergence to the true solution and the stability of convergence process.Through a comprehensive evaluation, we demonstrate that uDDDMs achieve FID scores comparable to the best-performing methods available for CIFAR-10 in both VP and VE. Specifically, uDDDM achieves one-step generation on CIFAR10 with FID of 2.63 and 2.53 for VE and VP respectively. By extending the sampling to 1000 steps, we further reduce FID score to 1.71 and 1.65 for VE and VP respectively, setting state-of-the-art performance in both cases.