# Abstract

**DDPM** model trained on [huggan/anime-faces](https://huggingface.co/datasets/huggan/anime-faces) dataset.

## Training Arguments

|          Argument           | Value  |
| :-------------------------: | :----: |
|         image_size          |   64   |
|      train_batch_size       |   16   |
|       eval_batch_size       |   16   |
|         num_epochs          |   50   |
| gradient_accumulation_steps |   1    |
|        learning_rate        |  1e-4  |
|       lr_warmup_steps       |  500   |
|       mixed_precision       | "fp16" |

For training code, please refer to [this link](https://github.com/LittleNyima/code-snippets/blob/master/ddpm-tutorial/ddpm_training.py).

# Inference

This project aims to implement DDPM from scratch, so `DDPMScheduler` is not used. Instead, I use only `UNet2DModel` and implement a simple scheduler myself. The inference code is:

```python
import torch
from tqdm import tqdm
from diffusers import UNet2DModel

class DDPM:
    def __init__(
        self,
        num_train_timesteps:int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
    ):
        self.num_train_timesteps = num_train_timesteps
        self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
        self.timesteps = torch.arange(num_train_timesteps - 1, -1, -1)
    
    def add_noise(
        self,
        original_samples: torch.Tensor,
        noise: torch.Tensor,
        timesteps: torch.Tensor,
    ):
        alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device ,dtype=original_samples.dtype)
        noise = noise.to(original_samples.device)
        timesteps = timesteps.to(original_samples.device)

        # \sqrt{\bar\alpha_t}
        sqrt_alpha_prod = alphas_cumprod[timesteps].flatten() ** 0.5
        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
        
        # \sqrt{1 - \bar\alpha_t}
        sqrt_one_minus_alpha_prod = (1.0 - alphas_cumprod[timesteps]).flatten() ** 0.5
        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
        
        return sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise

    @torch.no_grad()
    def sample(
        self,
        unet: UNet2DModel,
        batch_size: int,
        in_channels: int,
        sample_size: int,
    ):
        betas = self.betas.to(unet.device)
        alphas = self.alphas.to(unet.device)
        alphas_cumprod = self.alphas_cumprod.to(unet.device)
        timesteps = self.timesteps.to(unet.device)
        images = torch.randn((batch_size, in_channels, sample_size, sample_size), device=unet.device)
        for timestep in tqdm(timesteps, desc='Sampling'):
            pred_noise: torch.Tensor = unet(images, timestep).sample

            # mean of q(x_{t-1}|x_t)
            alpha_t = alphas[timestep]
            alpha_cumprod_t = alphas_cumprod[timestep]
            sqrt_alpha_t = alpha_t ** 0.5
            one_minus_alpha_t = 1.0 - alpha_t
            sqrt_one_minus_alpha_cumprod_t = (1 - alpha_cumprod_t) ** 0.5
            mean = (images - one_minus_alpha_t / sqrt_one_minus_alpha_cumprod_t * pred_noise) / sqrt_alpha_t
            
            # variance of q(x_{t-1}|x_t)
            if timestep > 1:
                beta_t = betas[timestep]
                one_minus_alpha_cumprod_t_minus_one = 1.0 - alphas_cumprod[timestep - 1]
                one_divided_by_sigma_square = alpha_t / beta_t + 1.0 / one_minus_alpha_cumprod_t_minus_one
                variance = (1.0 / one_divided_by_sigma_square) ** 0.5
            else:
                variance = torch.zeros_like(timestep)
            
            epsilon = torch.randn_like(images)
            images = mean + variance * epsilon
        images = (images / 2.0 + 0.5).clamp(0, 1).cpu().permute(0, 2, 3, 1).numpy()
        return images

model = UNet2DModel.from_pretrained('ddpm-animefaces-64').cuda()
ddpm = DDPM()
images = ddpm.sample(model, 32, 3, 64)

from diffusers.utils import make_image_grid, numpy_to_pil
image_grid = make_image_grid(numpy_to_pil(images), rows=4, cols=8)
image_grid.save('ddpm-sample-results.png')
```

This can also be found in [this link](https://github.com/LittleNyima/code-snippets/blob/master/ddpm-tutorial/ddpm_sampling.py).