You write custom CUDA kernels to replace the PyTorch operators in the given Pairwise Euclidean Distance architecture to get speedups.
You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace the combined broadcasting subtraction and L2 norm operators with a custom CUDA kernel (considering operator fusion opportunities to combine the element-wise difference calculation, sum of squares, and square root into a single kernel) or adjust algorithms for better performance. You are only limited by your imagination.

Here's an example to show you the syntax of inline embedding custom CUDA operators in PyTorch (for reference of code structure, not functional alignment):
The example given architecture (sample structure):
import torch
import torch.nn as nn
import torch.nn.functional as F
class Model(nn.Module):
    def __init__(self) -> None:
        super().__init__()
    def forward(self, a, b):
        return a + b
def get_inputs():
    # randomly generate input tensors based on the model architecture
    a = torch.randn(1, 128).cuda()
    b = torch.randn(1, 128).cuda()
    return [a, b]
def get_init_inputs():
    # randomly generate tensors required for initialization based on the model architecture
    return []

The example new arch with custom CUDA kernels (sample structure):
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline
# Define custom CUDA kernel and load it inline
custom_add_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
__global__ void custom_add_kernel(const float* a, const float* b, float* out, int size) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) {
        out[idx] = a[idx] + b[idx];
    }
}
torch::Tensor custom_add_cuda(torch::Tensor a, torch::Tensor b) {
    auto size = a.numel();
    auto out = torch::empty_like(a);
    const int block_size = 256;
    int num_blocks = (size + block_size - 1) / block_size;
    custom_add_kernel<<<num_blocks, block_size>>>(a.data_ptr<float>(), b.data_ptr<float>(), out.data_ptr<float>(), size);
    return out;
}
"""
custom_add_cpp_source = "torch::Tensor custom_add_cuda(torch::Tensor a, torch::Tensor b);"
custom_add = load_inline(
    name="custom_add",
    cpp_sources=custom_add_cpp_source,
    cuda_sources=custom_add_source,
    functions=["custom_add_cuda"],
    verbose=True
)
class Model(nn.Module):
    def __init__(self) -> None:
        super().__init__()
        self.custom_add = custom_add
    def forward(self, a, b):
        return self.custom_add.custom_add_cuda(a, b)
def get_inputs():
    # randomly generate input tensors based on the model architecture
    a = torch.randn(1, 128).cuda()
    b = torch.randn(1, 128).cuda()
    return [a, b]
def get_init_inputs():
    # randomly generate tensors required for initialization based on the model architecture
    return []

You are given the following Pairwise Euclidean Distance architecture (base PyTorch implementation):
import torch
import torch.nn as nn
class Model(nn.Module):
    """
    Pairwise Euclidean Distance function: Mathematical formulation is ||x_i - y_j||_2 for each pair (x_i, y_j),
    where x_i is the i-th vector in input x (shape (N, D)), y_j is the j-th vector in input y (shape (M, D)),
    and ||·||_2 denotes the L2 norm (Euclidean distance).
    """
    def __init__(self):
        super(Model, self).__init__()
    
    def forward(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """
        Computes the pairwise Euclidean distance matrix between two sets of vectors.
        Args:
            x (torch.Tensor): Input tensor with fixed shape (N, D)
                              where N=1024 (number of vectors in first set) and D=512 (dimensionality of each vector).
            y (torch.Tensor): Input tensor with fixed shape (M, D)
                              where M=1024 (number of vectors in second set) and D=512 (dimensionality of each vector).
        Returns:
            torch.Tensor: Output tensor of shape (N, M) where each element [i, j] is the Euclidean distance between x[i] and y[j].
        """
        # x.unsqueeze(1) -> (N, 1, D), y.unsqueeze(0) -> (1, M, D)
        # Broadcasting subtraction results in (N, M, D)
        diff = x.unsqueeze(1) - y.unsqueeze(0)
        # Compute L2 norm along the last dimension to get (N, M) distance matrix
        dist_matrix = torch.norm(diff, p=2, dim=-1)
        return dist_matrix

# Fixed hyperparameters for input generation
N = 1024  # Number of vectors in the first set
M = 1024  # Number of vectors in the second set
D = 512   # Dimensionality of each vector

def get_inputs():
    # Randomly generate input tensors matching the fixed shapes (N, D) and (M, D)
    x = torch.randn(N, D)
    y = torch.randn(M, D)
    return [x, y]

def get_init_inputs():
    # No special initialization tensors needed (model has no trainable parameters)
    return []