import torch
import torch.nn.functional as F

def gaussian_blur_2d(x, radius: float):
    if radius <= 0:
        return x

    sigma = radius * 0.5
    k = int(max(3, radius * 2 + 1))
    if k % 2 == 0:
        k += 1

    device = x.device

    coords = torch.arange(k, device=device) - k // 2
    g = torch.exp(-(coords ** 2) / (2 * sigma ** 2))
    g = g / g.sum()

    # reshape for separable conv
    g_h = g.view(1, 1, 1, k)
    g_v = g.view(1, 1, k, 1)

    x = x.unsqueeze(1)  # [B,1,H,W]

    # IMPORTANT: symmetric SAME padding
    pad = k // 2

    x = F.conv2d(x, g_h, padding=(0, pad))
    x = F.conv2d(x, g_v, padding=(pad, 0))

    return x.squeeze(1)