def welsch_loss(img1: Tensor, img2: Tensor, reduction: str = "none") -> Tensor:
    r"""Criterion that computes the Welsch [2] (aka. Leclerc [3]) loss.

    According to [1], we compute the Welsch loss as follows:

    .. math::

        \text{WL}(x, y) = 1 - exp(-\frac{1}{2} (x - y)^{2})

    Where:
       - :math:`x` is the prediction.
       - :math:`y` is the target to be regressed to.

    Reference:
        [1] https://arxiv.org/pdf/1701.03077.pdf
        [2] https://www.tandfonline.com/doi/abs/10.1080/03610917808812083
        [3] https://link.springer.com/article/10.1007/BF00054839

    Args:
        img1: the predicted tensor with shape :math:`(*)`.
        img2: the target tensor with the same shape as img1.
        reduction: Specifies the reduction to apply to the
          output: ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction
          will be applied (default), ``'mean'``: the sum of the output will be divided
          by the number of elements in the output, ``'sum'``: the output will be
          summed.

    Return:
        a scalar with the computed loss.

    Example:
        >>> img1 = torch.randn(2, 3, 32, 32, requires_grad=True)
        >>> img2 = torch.randn(2, 3, 32, 32)
        >>> output = welsch_loss(img1, img2, reduction="mean")
        >>> output.backward()

    """
    KORNIA_CHECK_IS_TENSOR(img1)

    KORNIA_CHECK_IS_TENSOR(img2)

    KORNIA_CHECK_SAME_SHAPE(img1, img2)

    KORNIA_CHECK_SAME_DEVICE(img1, img2)

    KORNIA_CHECK(reduction in ("mean", "sum", "none"), f"Given type of reduction is not supported. Got: {reduction}")

    # compute loss
    loss = 1.0 - (-0.5 * (img1 - img2) ** 2).exp()

    # perform reduction
    if reduction == "mean":
        loss = loss.mean()
    elif reduction == "sum":
        loss = loss.sum()
    elif reduction == "none":
        pass
    else:
        raise NotImplementedError("Invalid reduction option.")

    return loss
Criterion that computes the Welsch [2] (aka. Leclerc [3]) loss.

    According to [1], we compute the Welsch loss as follows:

    .. math::

        \text{WL}(x, y) = 1 - exp(-\frac{1}{2} (x - y)^{2})

    Where:
       - :math:`x` is the prediction.
       - :math:`y` is the target to be regressed to.

    Reference:
        [1] https://arxiv.org/pdf/1701.03077.pdf
        [2] https://www.tandfonline.com/doi/abs/10.1080/03610917808812083
        [3] https://link.springer.com/article/10.1007/BF00054839

    Args:
        img1: the predicted tensor with shape :math:`(*)`.
        img2: the target tensor with the same shape as img1.
        reduction: Specifies the reduction to apply to the
          output: ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction
          will be applied (default), ``'mean'``: the sum of the output will be divided
          by the number of elements in the output, ``'sum'``: the output will be
          summed.

    Return:
        a scalar with the computed loss.

    Example:
        >>> img1 = torch.randn(2, 3, 32, 32, requires_grad=True)
        >>> img2 = torch.randn(2, 3, 32, 32)
        >>> output = welsch_loss(img1, img2, reduction="mean")
        >>> output.backward()

    
kornia/losses/welsch.py