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<p align="center">
<img alt="banner" src="./assets/banner.webp">
</p>

---

# PyTorch Implementation of Denoising Diffusion Probabilistic Models [[paper]](https://arxiv.org/abs/2006.11239) [[official repo]](https://github.com/hojonathanho/diffusion)

## Code usage
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### Toy data

#### 8 Gaussian
<p align="center"> <img alt="gaussian8" src="./assets/gaussian8.gif" /> </p>

<details>
<summary>Animation</summary>
<p align="center">
<img alt="gaussian8" src="./assets/gaussian8.webp" height=360 width=360 />
</p>
</details>

#### 25 Gaussian
<p align="center"> <img alt="gaussian25" src="./assets/gaussian25.gif" /> </p>
<details>
<summary>Animation</summary>
<p align="center">
<img alt="gaussian25" src="./assets/gaussian25.webp" height=360 width=360 />
</p>
</details>

#### Swiss Roll
<p align="center"> <img alt="swissroll" src="./assets/swissroll.gif" /> </p>
<details>
<summary>Animation</summary>
<p align="center">
<img alt="swissroll" src="./assets/swissroll.webp" height=360 width=360 />
</p>
</details>

### Real-world data

*Table of evaluation metrics*

|Dataset|FID (↓)|Precision (↑)|Recall (↑)|Training steps|Training loss|
|:---:|:---:|:---:|:---:|:---:|:---:|
|CIFAR-10|11.11|0.738|0.421|46.8k|0.0296|
|\|__|6.45|0.727|0.480|93.6k|0.0294|
|\|__|4.99|0.727|0.503|140.4k|0.0287|
|\|__|4.48|0.730|0.517|187.2k|0.0289|
|\|__|4.07|0.731|**0.524**|234.0k|0.0286|
|\|__|**4.01**|**0.733**|0.520|280.8k|**0.0285**|
|CelebA|4.45|0.778|0.478|237.3k|0.0154|
|CIFAR-10|11.32|0.732|0.422|46.8k|0.0301|
|\|__|6.49|0.732|0.474|93.6k|0.0293|
|\|__|5.10|0.727|0.502|140.4k|0.0290|
|\|__|4.43|0.727|0.518|187.2k|0.0285|
|\|__|4.13|0.732|0.526|234.0k|0.0285|
|\|__|3.88|0.729|**0.527**|280.8k|0.0286|
|\|__|3.99|0.736|0.523|327.6k|0.0286|
|\|__|3.95|0.737|0.523|374.4k|**0.0283**|
|\|__|**3.83**|**0.743**|0.526|421.2k|0.0283|
|CelebA|5.38|**0.782**|0.459|158.2k|0.0156|
|\|__|**4.27**|0.769|**0.500**|316.4k|**0.0151**|

#### CIFAR-10 [[checkpoint]](https://github.com/tqch/ddpm-torch/releases/download/checkpoints/ddpm_cifar10_720.pt)

##### Training samples (720 epochs)
<p align="center"> <img alt="cifar10_train_100" src="./assets/cifar10_train_720.webp" /> </p>
#### CIFAR-10 [[checkpoint]](https://github.com/tqch/ddpm-torch/releases/download/checkpoints/ddpm_cifar10_1080.pt)

##### Denoising process
<p align="center"> <img alt="cifar10_denoise_100" src="./assets/cifar10_denoise_100.webp" /></p>
<details>
<summary>Training samples (1080 epochs)</summary>
<p align="center">
<img alt="cifar10_train_100" src="./assets/cifar10_train_1080.webp" />
</p>
</details>

#### CelebA [[checkpoint]](https://github.com/tqch/ddpm-torch/releases/download/checkpoints/ddpm_celeba_150.pt)
<details>
<summary>Denoising process</summary>
<p align="center">
<img alt="cifar10_denoise_100"src="./assets/cifar10_denoise_100.webp" />
</p>
</details>

##### Training samples (150 epochs)
<p align="center"> <img alt="celeba_train_100" src="./assets/celeba_train_150.webp" /> </p>
#### CelebA [[checkpoint]](https://github.com/tqch/ddpm-torch/releases/download/checkpoints/ddpm_celeba_200.pt)

##### Denoising process
<p align="center"> <img alt="celeba_denoise_100" src="./assets/celeba_denoise_100.webp" /> </p>
<details>
<summary>Training samples (200 epochs)</summary>
<p align="center">
<img alt="cifar10_train_100" src="./assets/celeba_train_200.webp" />
</p>
</details>

<details>
<summary>Denoising process</summary>
<p align="center">
<img alt="cifar10_denoise_100"src="./assets/celeba_denoise_100.webp" />
</p>
</details>

## Reference formulae

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