def append_dims(x, target_dims):
    """Appends dimensions to the end of a tensor until it has target_dims dimensions.
    From https://github.com/crowsonkb/k-diffusion/blob/master/k_diffusion/utils.py"""
    dims_to_append = target_dims - x.ndim
    if dims_to_append < 0:
        raise ValueError(f"input has {x.ndim} dims but target_dims is {target_dims}, which is less")
    return x[(...,) + (None,) * dims_to_append]


def norm_thresholding(x0, value):
    s = append_dims(x0.pow(2).flatten(1).mean(1).sqrt().clamp(min=value), x0.ndim)
    return x0 * (value / s)


def spatial_norm_thresholding(x0, value):
    # b c h w
    s = x0.pow(2).mean(1, keepdim=True).sqrt().clamp(min=value)
    return x0 * (value / s)
