---
title: "Denoising Diffusion Implicit Models — Song 2020"
description: "Diffusion-based image generators such as DDPM produce samples rivaling GANs, but generation is very slow because the reverse chain must run through every…"
authors: ["Jiaming Song", "Chenlin Meng", "Stefano Ermon"]
year: 2020
venue: "arXiv:2010.02502"
source: "https://arxiv.org/abs/2010.02502"
doi: "10.48550/arxiv.2010.02502"
arxiv: "2010.02502"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/song-2020-denoising-diffusion-implicit-models/"
---
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# Denoising Diffusion Implicit Models

**Authors:** Jiaming Song, Chenlin Meng, [Stefano Ermon](https://md.research.elamur.ai/free/en/authors/stefano-ermon/) · **Year:** 2020 · **Venue:** arXiv:2010.02502 · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2010.02502) · [PDF](https://arxiv.org/pdf/2010.02502) · [DOI 10.48550/arxiv.2010.02502](https://doi.org/10.48550/arxiv.2010.02502) · [arXiv 2010.02502](https://arxiv.org/abs/2010.02502) · [OpenAlex](https://openalex.org/W3092442149)

**Citations:** 100 citations (openalex-snapshot · 2026-10-14) · [360](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
Diffusion-based image generators such as DDPM produce samples rivaling GANs, but generation is very slow because the reverse chain must run through every step of a long noising process, typically T = 1000. The authors propose DDIM, which keeps the DDPM training procedure but changes how samples are drawn. They note that the DDPM loss depends only on per-step marginals of the noising process, not on its full joint distribution. This lets them build a family of non-Markovian forward processes, controlled by a variance parameter σ, that share the same surrogate objective. Setting σ to zero gives a deterministic, implicit generator that can skip timesteps and sample along a short sub-sequence. A model trained once as a DDPM can therefore be reused without retraining. On CIFAR10, CelebA and LSUN, DDIM keeps sample quality much better than DDPM when steps are cut sharply, achieving 10× to 50× wall-clock speedups. Its deterministic latent mapping also enables meaningful interpolation and accurate reconstruction, which makes diffusion models far more practical.

## Key points
- **Motivating cost:** drawing 50k 32×32 images from a DDPM takes about 20 hours on an Nvidia 2080 Ti, while a GAN needs under a minute. At 256×256 resolution, the DDPM time approaches 1000 hours.
- **Theorem 1:** for every σ > 0, the variational objective J_σ equals a weighted DDPM loss L_γ up to a constant. The parameter η interpolates between deterministic DDIM (η = 0) and DDPM-like sampling (η = 1).
- **Experimental setup:** experiments use CIFAR10 (32×32), CelebA (64×64), LSUN Bedroom and LSUN Church (both 256×256). The models are pretrained DDPM U-Net (Wide ResNet) checkpoints, except CelebA, which the authors trained themselves.
- **Results with 20 sampling steps (FID):**
  - LSUN Bedroom: DDIM 8.89 vs DDPM 22.77.
  - LSUN Church: DDIM 12.47 vs DDPM 23.37.
  - For reference, 1000-step DDPM scores 6.36 (Bedroom) and 7.89 (Church).
  - At 100 steps on Church, DDPM is slightly better (8.27 vs 10.58).
- **Consistency:** the same initial x_T yields images with similar high-level features regardless of chain length. Spherical linear interpolation (slerp) of x_T values produces smooth semantic interpolations.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

Fields: [Other](https://md.research.elamur.ai/free/en/shelves/other/)

## Cited by

Cited by

360 papers of our library cite it (of the 140673 whose bibliographies we read); 9 of them have a page here, 351 not yet.

- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://md.research.elamur.ai/free/en/papers/austin-2021-structured-denoising-diffusion-models-discrete/)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://md.research.elamur.ai/free/en/papers/dong-2023-raft-reward-ranked-finetuning-generative/)
- [DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models](https://md.research.elamur.ai/free/en/papers/gong-2023-diffuseq-v2-bridging-discrete-continuous/)
- [Flow Matching for Generative Modeling](https://md.research.elamur.ai/free/en/papers/lipman-2022-flow-matching-generative-modeling/)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://md.research.elamur.ai/free/en/papers/liu-2022-flow-straight-fast-learning-generate/)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://md.research.elamur.ai/free/en/papers/podell-2023-sdxl-improving-latent-diffusion-models/)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://md.research.elamur.ai/free/en/papers/ramesh-2022-hierarchical-text-conditional-image-generation/)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://md.research.elamur.ai/free/en/papers/saharia-2022-photorealistic-text-image-diffusion-models/)
- [Can Diffusion Model Achieve Better Performance in Text Generation ? Bridging the Gap between Training and Inference !](https://md.research.elamur.ai/free/en/papers/tang-2023-can-diffusion-model-achieve-better/)

## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{song2020denoising,
  title = {{Denoising Diffusion Implicit Models}},
  author = {Song, Jiaming and Meng, Chenlin and Ermon, Stefano},
  year = {2020},
  doi = {10.48550/arxiv.2010.02502},
  eprint = {2010.02502},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2010.02502}
}
```

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