Implementation:Kornia Kornia Charbonnier Loss

Knowledge Sources	Kornia
Domains	Vision, Loss_Functions
Last Updated	2026-02-09 15:00 GMT

Overview

Charbonnier Loss (also known as L1-L2 loss) is a differentiable approximation of the L1 loss that provides smooth gradients near zero.

Description

The Charbonnier loss, also known as the pseudo-Huber loss or L1-L2 loss, is a smooth approximation of L1 loss that is differentiable everywhere, including at zero. It combines the properties of both L1 and L2 losses: it behaves like L2 for small residuals (providing smooth gradients) and like L1 for large residuals (providing robustness to outliers).

The mathematical formulation following Barron (2019) is:

$\text{CL}(x,y)=\sqrt{(x-y{)}^2+1}-1$

Where $x$ is the prediction and $y$ is the target. The loss is always non-negative and provides a smooth transition between quadratic and linear behavior.

Usage

Import this loss for image restoration tasks such as super-resolution, denoising, and deblurring where you want a robust loss that provides smooth gradients. It is commonly used as an alternative to L1 loss in training deep neural networks for pixel-level regression.

Code Reference

Source Location

• Repository: Kornia
• File: kornia/losses/charbonnier.py
• Lines: 1-145

Signature

def charbonnier_loss(
    img1: torch.Tensor,
    img2: torch.Tensor,
    reduction: str = "none",
) -> torch.Tensor: ...

class CharbonnierLoss(nn.Module):
    def __init__(self, reduction: str = "none") -> None: ...
    def forward(self, img1: torch.Tensor, img2: torch.Tensor) -> torch.Tensor: ...

Import

from kornia.losses import CharbonnierLoss
from kornia.losses import charbonnier_loss

I/O Contract

Inputs

Name	Type	Required	Description
img1	torch.Tensor	Yes	Predicted tensor with arbitrary shape (*)
img2	torch.Tensor	Yes	Target tensor with the same shape as img1
reduction	str	No	Reduction mode: 'none' (default), 'mean', or 'sum'

Outputs

Name	Type	Description
loss	torch.Tensor	Computed Charbonnier loss; element-wise for 'none', scalar for 'mean'/'sum'

Usage Examples

import torch
from kornia.losses import CharbonnierLoss

# Create sample tensors
img1 = torch.randn(2, 3, 32, 32, requires_grad=True)
img2 = torch.randn(2, 3, 32, 32)

# Using the module API
criterion = CharbonnierLoss(reduction="mean")
output = criterion(img1, img2)
output.backward()

# Using the functional API
from kornia.losses import charbonnier_loss
output = charbonnier_loss(img1, img2, reduction="sum")

Related Pages

• Principle:Kornia_Kornia_Robust_Loss_Functions