---
title: Kernel Inception Distance
description: >-
  Calculate Kernel Inception Distance (KID) which is used to access the quality
  of generated images.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/image/kernel_inception_distance'
---
# Kernel Inception Distance {#kernel-inception-distance}

## Module Interface {#module-interface}

### `class torchmetrics.image.kid.KernelInceptionDistance(feature=2048, subsets=100, subset_size=1000, degree=3, gamma=None, coef=1.0, reset_real_features=True, normalize=False, **kwargs)` {#torchmetrics.image.kid.KernelInceptionDistance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/kid.py#L71-L358)

Calculate Kernel Inception Distance (KID) which is used to access the quality of generated images.

```math
KID = MMD(f_{real}, f_{fake})^2
```

where $`MMD`$ is the maximum mean discrepancy and $`I_{real}, I_{fake}`$ are extracted features from real and fake images, see [kid ref1](https://arxiv.org/abs/1801.01401) for more details. In particular, calculating the MMD requires the evaluation of a polynomial kernel function $`k`$

```math
k(x,y) = (\gamma * x^T y + coef)^{degree}
```

which controls the distance between two features. In practise the MMD is calculated over a number of subsets to be able to both get the mean and standard deviation of KID.

Using the default feature extraction (Inception v3 using the original weights from [kid ref2](https://arxiv.org/abs/1706.08500)), the input is expected to be mini-batches of 3-channel RGB images of shape `(3xHxW)`. If argument `normalize` is `True` images are expected to be dtype `float` and have values in the `[0,1]` range, else if `normalize` is set to `False` images are expected to have dtype `uint8` and take values in the `[0, 255]` range. All images will be resized to 299 x 299 which is the size of the original training data. The boolian flag `real` determines if the images should update the statistics of the real distribution or the fake distribution.

Using custom feature extractor is also possible. One can give a torch.nn.Module as feature argument. This custom feature extractor is expected to have output shape of `(1, num_features)` This would change the used feature extractor from default (Inception v3) to the given network. `normalize` argument won’t have any effect and update method expects to have the tensor given to imgs argument to be in the correct shape and type that is compatible to the custom feature extractor.

Hint

Using this metric with the default feature extractor requires that `torch-fidelity` is installed. Either install as `pip install torchmetrics[image]` or `pip install torch-fidelity`

As input to `forward` and `update` the metric accepts the following input

*   `imgs` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): tensor with images feed to the feature extractor of shape `(N,C,H,W)`
    
*   `real` (bool): bool indicating if `imgs` belong to the real or the fake distribution
    

As output of forward and compute the metric returns the following output

*   `kid_mean` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): float scalar tensor with mean value over subsets
    
*   `kid_std` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): float scalar tensor with standard deviation value over subsets
    

Parameters:

*   **feature** (`Union`\[[`str`](https://docs.python.org/3/builtins/stdtypes.html#str "(in Python v3.15)"), [`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`Module`](https://docs.pytorch.org/docs/stable/generated/torch.nn.Module.html#torch.nn.Module "(in PyTorch v2.15)")\]) –
    
    Either an str, integer or `nn.Module`:
    
    *   an str or integer will indicate the inceptionv3 feature layer to choose. Can be one of the following: ‘logits\_unbiased’, 64, 192, 768, 2048
        
    *   an `nn.Module` for using a custom feature extractor. Expects that its forward method returns an `(N,d)` matrix where `N` is the batch size and `d` is the feature size.
        
    
*   **subsets** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of subsets to calculate the mean and standard deviation scores over
    
*   **subset\_size** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of randomly picked samples in each subset
    
*   **degree** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Degree of the polynomial kernel function
    
*   **gamma** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\]) – Scale-length of polynomial kernel. If set to `None` will be automatically set to the feature size
    
*   **coef** ([`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")) – Bias term in the polynomial kernel.
    
*   **reset\_real\_features** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – Whether to also reset the real features. Since in many cases the real dataset does not change, the features can cached them to avoid recomputing them which is costly. Set this to `False` if your dataset does not change.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Raises:

*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `feature` is set to an `int` (default settings) and `torch-fidelity` is not installed
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `feature` is set to an `int` not in `(64, 192, 768, 2048)`
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `subsets` is not an integer larger than 0
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `subset_size` is not an integer larger than 0
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `degree` is not an integer larger than 0
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `gamma` is neither `None` or a float larger than 0
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `coef` is not an float larger than 0
    
*   [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError "(in Python v3.15)") – If `reset_real_features` is not an `bool`
    

Example

```python
>>> from torch import randint
>>> from torchmetrics.image.kid import KernelInceptionDistance
>>> kid = KernelInceptionDistance(subset_size=50)
>>> # generate two slightly overlapping image intensity distributions
>>> imgs_dist1 = randint(0, 200, (100, 3, 299, 299), dtype=torch.uint8)
>>> imgs_dist2 = randint(100, 255, (100, 3, 299, 299), dtype=torch.uint8)
>>> kid.update(imgs_dist1, real=True)
>>> kid.update(imgs_dist2, real=False)
>>> kid.compute()
(tensor(0.0312), tensor(0.0025))
```

#### `plot(val=None, ax=None)` {#torchmetrics.image.kid.KernelInceptionDistance.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/kid.py#L309-L358)

Plot a single or multiple values from the metric.

Parameters:

*   **val** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> # Example plotting a single value
>>> import torch
>>> from torchmetrics.image.kid import KernelInceptionDistance
>>> imgs_dist1 = torch.randint(0, 200, (30, 3, 299, 299), dtype=torch.uint8)
>>> imgs_dist2 = torch.randint(100, 255, (30, 3, 299, 299), dtype=torch.uint8)
>>> metric = KernelInceptionDistance(subsets=3, subset_size=20)
>>> metric.update(imgs_dist1, real=True)
>>> metric.update(imgs_dist2, real=False)
>>> fig_, ax_ = metric.plot()
```

```python
>>> # Example plotting multiple values
>>> import torch
>>> from torchmetrics.image.kid import KernelInceptionDistance
>>> imgs_dist1 = lambda: torch.randint(0, 200, (30, 3, 299, 299), dtype=torch.uint8)
>>> imgs_dist2 = lambda: torch.randint(100, 255, (30, 3, 299, 299), dtype=torch.uint8)
>>> metric = KernelInceptionDistance(subsets=3, subset_size=20)
>>> values = [ ]
>>> for _ in range(3):
...     metric.update(imgs_dist1(), real=True)
...     metric.update(imgs_dist2(), real=False)
...     values.append(metric.compute()[0])
...     metric.reset()
>>> fig_, ax_ = metric.plot(values)
```

#### `reset()` {#torchmetrics.image.kid.KernelInceptionDistance.reset}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/kid.py#L299-L307)

Reset metric states.

Return type:

[`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")

---

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