---
title: Frechet Inception Distance (FID)
description: >-
  Calculate Fréchet inception distance (FID) which is used to assess the quality
  of generated images.
canonical: 'https://lightning.ai/docs/torchmetrics/stable/image/frechet_inception_distance'
---
# Frechet Inception Distance (FID) {#frechet-inception-distance-fid}

## Module Interface {#module-interface}

### `class torchmetrics.image.fid.FrechetInceptionDistance(feature=2048, reset_real_features=True, normalize=False, input_img_size=(3, 299, 299), feature_extractor_weights_path=None, antialias=True, **kwargs)` {#torchmetrics.image.fid.FrechetInceptionDistance}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/fid.py#L197-L495)

Calculate Fréchet inception distance ([FID](https://en.wikipedia.org/wiki/Fr%C3%A9chet_inception_distance)) which is used to assess the quality of generated images.

```math
FID = \|\mu - \mu_w\|^2 + tr(\Sigma + \Sigma_w - 2(\Sigma \Sigma_w)^{\frac{1}{2}})
```

where $`\mathcal{N}(\mu, \Sigma)`$ is the multivariate normal distribution estimated from Inception v3 ([fid ref1](https://arxiv.org/abs/1512.00567)) features calculated on real life images and $`\mathcal{N}(\mu_w, \Sigma_w)`$ is the multivariate normal distribution estimated from Inception v3 features calculated on generated (fake) images. The metric was originally proposed in [fid ref1](https://arxiv.org/abs/1512.00567).

Using the default feature extraction (Inception v3 using the original weights from [fid 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. In case network doesn’t have `num_features` attribute, a random tensor will be given to the network to infer feature dimensionality. Size of this tensor can be controlled by `input_img_size` argument and type of the tensor can be controlled with `normalize` argument (`True` uses float32 tensors and `False` uses int8 tensors). In this case, 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.

This metric is known to be unstable in its calculatations, and we recommend for the best results using this metric that you calculate using torch.float64 (default is torch.float32) which can be set using the .set\_dtype method of the metric.

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 with
    
*   `real` ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")): bool indicating if `imgs` belong to the real or the fake distribution
    

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

*   `fid` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): float scalar tensor with mean FID value over samples
    

Parameters:

*   **feature** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`Module`](https://docs.pytorch.org/docs/stable/generated/torch.nn.Module.html#torch.nn.Module "(in PyTorch v2.15)")\]) –
    
    Either an integer or `nn.Module`:
    
    *   an integer will indicate the inceptionv3 feature layer to choose. Can be one of the following: 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.
        
    
*   **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 be cached them to avoid recomputing them which is costly. Set this to `False` if your dataset does not change.
    
*   **normalize** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) –
    
    Argument for controlling the input image dtype normalization:
    
    *   If default feature extractor is used, controls whether input imgs have values in range \[0, 1\] or not:
        
        *   True: if input imgs have values ranged in \[0, 1\]. They are cast to int8/byte tensors.
            
        *   False: if input imgs have values ranged in \[0, 255\]. No casting is done.
            
    *   If custom feature extractor module is used, controls type of the input img tensors:
        
        *   True: if input imgs are expected to be in the data type of torch.float32.
            
        *   False: if input imgs are expected to be in the data type of torch.int8.
            
    
*   **input\_img\_size** ([`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – tuple of integers. Indicates input img size to the custom feature extractor network if provided.
    
*   **use\_antialias** – boolian flag to indicate whether to use antialiasing when resizing images. This will change the resize function to use bilinear interpolation with antialiasing, which is different from the original Inception v3 implementation. Does not apply to custom feature extractor networks.
    
*   **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 torch version is lower than 1.9
    
*   [**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(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 \[64, 192, 768, 2048\]
    
*   [**TypeError**](https://docs.python.org/3/builtins/exceptions.html#TypeError "(in Python v3.15)") – If `feature` is not an `str`, `int` or `torch.nn.Module`
    
*   [**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 rand
>>> from torchmetrics.image.fid import FrechetInceptionDistance
>>> fid = FrechetInceptionDistance(feature=64)
>>> # generate two slightly overlapping image intensity distributions
>>> imgs_dist1 = torch.randint(0, 200, (100, 3, 299, 299), dtype=torch.uint8)
>>> imgs_dist2 = torch.randint(100, 255, (100, 3, 299, 299), dtype=torch.uint8)
>>> fid.update(imgs_dist1, real=True)
>>> fid.update(imgs_dist2, real=False)
>>> fid.compute()
tensor(12.6388)
```

#### `plot(val=None, ax=None)` {#torchmetrics.image.fid.FrechetInceptionDistance.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/fid.py#L447-L495)

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.fid import FrechetInceptionDistance
>>> imgs_dist1 = torch.randint(0, 200, (100, 3, 299, 299), dtype=torch.uint8)
>>> imgs_dist2 = torch.randint(100, 255, (100, 3, 299, 299), dtype=torch.uint8)
>>> metric = FrechetInceptionDistance(feature=64)
>>> 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.fid import FrechetInceptionDistance
>>> imgs_dist1 = lambda: torch.randint(0, 200, (100, 3, 299, 299), dtype=torch.uint8)
>>> imgs_dist2 = lambda: torch.randint(100, 255, (100, 3, 299, 299), dtype=torch.uint8)
>>> metric = FrechetInceptionDistance(feature=64)
>>> values = [ ]
>>> for _ in range(3):
...     metric.update(imgs_dist1(), real=True)
...     metric.update(imgs_dist2(), real=False)
...     values.append(metric.compute())
...     metric.reset()
>>> fig_, ax_ = metric.plot(values)
```

#### `reset()` {#torchmetrics.image.fid.FrechetInceptionDistance.reset}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/fid.py#L422-L433)

Reset metric states.

Return type:

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

#### `set_dtype(dst_type)` {#torchmetrics.image.fid.FrechetInceptionDistance.set_dtype}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/image/fid.py#L435-L445)

Transfer all metric state to specific dtype. Special version of standard type method.

Parameters:

**dst\_type** (`Union`\[[`str`](https://docs.python.org/3/builtins/stdtypes.html#str "(in Python v3.15)"), [`dtype`](https://docs.pytorch.org/docs/stable/tensor_attributes.html#torch.dtype "(in PyTorch v2.15)")\]) – the desired type as `torch.dtype` or string

Return type:

[`Metric`](/docs/torchmetrics/1.9.0/api-reference/metric.md#torchmetrics.Metric "torchmetrics.metric.Metric")

---

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