[Community Pipeline] Diffusion Posterior Sampling for General Noisy Inverse Problems (#5939)

* [community pipeline] dps impl

* add type checking

* pass ruff check

* ruff formatter

examples/community/README.md

@@ -2481,3 +2481,145 @@ images = pipe(
 images[0].save("controlnet_and_adapter_inpaint.png")
 
 ```
+
+## Diffusion Posterior Sampling Pipeline
+* Reference paper
+    ```
+    @article{chung2022diffusion,
+    title={Diffusion posterior sampling for general noisy inverse problems},
+    author={Chung, Hyungjin and Kim, Jeongsol and Mccann, Michael T and Klasky, Marc L and Ye, Jong Chul},
+    journal={arXiv preprint arXiv:2209.14687},
+    year={2022}
+    }
+    ```
+* This pipeline allows zero-shot conditional sampling from the posterior distribution $p(x|y)$, given observation on $y$, unconditional generative model $p(x)$ and differentiable operator $y=f(x)$.
+* For example, $f(.)$ can be downsample operator, then $y$ is a downsampled image, and the pipeline becomes a super-resolution pipeline.
+* To use this pipeline, you need to know your operator $f(.)$ and corrupted image $y$, and pass them during the call. For example, as in the main function of dps_pipeline.py, you need to first define the Gaussian blurring operator $f(.)$. The operator should be a callable nn.Module, with all the parameter gradient disabled:
+    ```python
+    import torch.nn.functional as F
+    import scipy
+    from torch import nn
+
+    # define the Gaussian blurring operator first
+    class GaussialBlurOperator(nn.Module):
+        def __init__(self, kernel_size, intensity):
+            super().__init__()
+
+            class Blurkernel(nn.Module):
+                def __init__(self, blur_type='gaussian', kernel_size=31, std=3.0):
+                    super().__init__()
+                    self.blur_type = blur_type
+                    self.kernel_size = kernel_size
+                    self.std = std
+                    self.seq = nn.Sequential(
+                        nn.ReflectionPad2d(self.kernel_size//2),
+                        nn.Conv2d(3, 3, self.kernel_size, stride=1, padding=0, bias=False, groups=3)
+                    )
+                    self.weights_init()
+
+                def forward(self, x):
+                    return self.seq(x)
+
+                def weights_init(self):
+                    if self.blur_type == "gaussian":
+                        n = np.zeros((self.kernel_size, self.kernel_size))
+                        n[self.kernel_size // 2,self.kernel_size // 2] = 1
+                        k = scipy.ndimage.gaussian_filter(n, sigma=self.std)
+                        k = torch.from_numpy(k)
+                        self.k = k
+                        for name, f in self.named_parameters():
+                            f.data.copy_(k)
+                    elif self.blur_type == "motion":
+                        k = Kernel(size=(self.kernel_size, self.kernel_size), intensity=self.std).kernelMatrix
+                        k = torch.from_numpy(k)
+                        self.k = k
+                        for name, f in self.named_parameters():
+                            f.data.copy_(k)
+
+                def update_weights(self, k):
+                    if not torch.is_tensor(k):
+                        k = torch.from_numpy(k)
+                    for name, f in self.named_parameters():
+                        f.data.copy_(k)
+
+                def get_kernel(self):
+                    return self.k
+                
+            self.kernel_size = kernel_size
+            self.conv = Blurkernel(blur_type='gaussian',
+                                kernel_size=kernel_size,
+                                std=intensity)
+            self.kernel = self.conv.get_kernel()
+            self.conv.update_weights(self.kernel.type(torch.float32))
+
+            for param in self.parameters():
+                param.requires_grad=False
+
+        def forward(self, data, **kwargs):
+            return self.conv(data)
+
+        def transpose(self, data, **kwargs):
+            return data
+
+        def get_kernel(self):
+            return self.kernel.view(1, 1, self.kernel_size, self.kernel_size)
+    ```
+* Next, you should obtain the corrupted image $y$ by the operator. In this example, we generate $y$ from the source image $x$. However in practice, having the operator $f(.)$ and corrupted image $y$ is enough:
+    ```python
+    # set up source image
+    src = Image.open('sample.png')
+    # read image into [1,3,H,W]
+    src = torch.from_numpy(np.array(src, dtype=np.float32)).permute(2,0,1)[None]
+    # normalize image to [-1,1]
+    src = (src / 127.5) - 1.0
+    src = src.to("cuda")
+
+    # set up operator and measurement
+    operator = GaussialBlurOperator(kernel_size=61, intensity=3.0).to("cuda")
+    measurement = operator(src)
+
+    # save the source and corrupted images
+    save_image((src+1.0)/2.0, "dps_src.png")
+    save_image((measurement+1.0)/2.0, "dps_mea.png")
+    ```
+* We provide an example pair of saved source and corrupted images, using the Gaussian blur operator above
+    * Source image:
+    * ![sample](https://github.com/tongdaxu/Images/assets/22267548/4d2a1216-08d1-4aeb-9ce3-7a2d87561d65)
+    * Gaussian blurred image:
+    * ![ddpm_generated_image](https://github.com/tongdaxu/Images/assets/22267548/65076258-344b-4ed8-b704-a04edaade8ae)
+    * You can download those image to run the example on your own.
+* Next, we need to define a loss function used for diffusion posterior sample. For most of the cases, the RMSE is fine:
+    ```python
+    def RMSELoss(yhat, y):
+        return torch.sqrt(torch.sum((yhat-y)**2))
+    ```
+* And next, as any other diffusion models, we need the score estimator and scheduler. As we are working with $256x256$ face images, we use ddmp-celebahq-256:
+    ```python
+    # set up scheduler
+    scheduler = DDPMScheduler.from_pretrained("google/ddpm-celebahq-256")
+    scheduler.set_timesteps(1000)
+
+    # set up model
+    model = UNet2DModel.from_pretrained("google/ddpm-celebahq-256").to("cuda")
+    ```
+* And finally, run the pipeline:
+    ```python
+    # finally, the pipeline
+    dpspipe = DPSPipeline(model, scheduler)
+    image = dpspipe(
+        measurement = measurement,
+        operator = operator,
+        loss_fn = RMSELoss,
+        zeta = 1.0,
+    ).images[0]
+    image.save("dps_generated_image.png")
+    ```
+* The zeta is a hyperparameter that is in range of $[0,1]$. It need to be tuned for best effect. By setting zeta=1, you should be able to have the reconstructed result:
+    * Reconstructed image:
+    * ![sample](https://github.com/tongdaxu/Images/assets/22267548/0ceb5575-d42e-4f0b-99c0-50e69c982209)
+* The reconstruction is perceptually similar to the source image, but different in details.
+* In dps_pipeline.py, we also provide a super-resolution example, which should produce:
+    * Downsampled image: 
+    * ![dps_mea](https://github.com/tongdaxu/Images/assets/22267548/ff6a33d6-26f0-42aa-88ce-f8a76ba45a13)
+    * Reconstructed image:
+    * ![dps_generated_image](https://github.com/tongdaxu/Images/assets/22267548/b74f084d-93f4-4845-83d8-44c0fa758a5f)