# How Much is Enough? A Study on Diffusion Times in Score-based Generative Models

arXiv: https://arxiv.org/abs/2206.05173 · HTML: https://mlsanity.com/paper/2206.05173/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)

## Built on by (most cited first, 30 of 35)

- [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)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [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)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [TFMQ-DM: Temporal Feature Maintenance Quantization for Diffusion Models](https://mlsanity.com/paper/2311.16503/) (2023)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Graph Generation with Diffusion Mixture](https://mlsanity.com/paper/2302.03596/) (2023)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Continuous-Time Functional Diffusion Processes](https://mlsanity.com/paper/2303.00800/) (2023)
- [MINDE: Mutual Information Neural Diffusion Estimation](https://mlsanity.com/paper/2310.09031/) (2023)
- [An analysis of the noise schedule for score-based generative models](https://mlsanity.com/paper/2402.04650/) (2024)
- [Improved Convergence of Score-Based Diffusion Models via Prediction-Correction](https://mlsanity.com/paper/2305.14164/) (2023)
- [Optimizing Diffusion Models for Joint Trajectory Prediction and Controllable Generation](https://mlsanity.com/paper/2408.00766/) (2024)
- [Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors](https://mlsanity.com/paper/2405.14250/) (2024)
- [Wasserstein proximal operators describe score-based generative models and resolve memorization](https://mlsanity.com/paper/2402.06162/) (2024)
- [Multi-modal Latent Diffusion](https://mlsanity.com/paper/2306.04445/) (2023)
- [Diffusion map particle systems for generative modeling](https://mlsanity.com/paper/2304.00200/) (2023)
- [TCAQ-DM: Timestep-Channel Adaptive Quantization for Diffusion Models](https://mlsanity.com/paper/2412.16700/) (2024)
- [Diffusion Model Quantization: A Review](https://mlsanity.com/paper/2505.05215/) (2025)
- [TwinDiffusion: Enhancing Coherence and Efficiency in Panoramic Image Generation with Diffusion Models](https://mlsanity.com/paper/2404.19475/) (2024)
- [Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics](https://mlsanity.com/paper/2406.13652/) (2024)
- [Temporal Feature Matters: A Framework for Diffusion Model Quantization](https://mlsanity.com/paper/2407.19547/) (2024)
- [On permutation symmetries in Bayesian neural network posteriors: a variational perspective](https://mlsanity.com/paper/2310.10171/) (2023)
- [SOmegaI: Score-based O-INFORMATION Estimation](https://mlsanity.com/paper/2402.05667/) (2024)
- [Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis](https://mlsanity.com/paper/2506.00849/) (2025)
- [Solving Prior Distribution Mismatch in Diffusion Models via Optimal Transport](https://mlsanity.com/paper/2410.13431/) (2024)
- [D2-DPM: Dual Denoising for Quantized Diffusion Probabilistic Models](https://mlsanity.com/paper/2501.08180/) (2025)

## Abstract (arXiv)

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.