# tensorplay.distributions.kl_divergence

Source: https://www.tensorplay.cn/docs/generated/tensorplay.distributions.kl_divergence.html

```python
tensorplay.distributions.kl_divergence(p: Distribution, q: Distribution) → Tensor
```

Compute Kullback-Leibler divergence $KL(p \| q)$ between two distributions.

$$KL(p \| q) = \int p(x) \log\frac {p(x)} {q(x)} \,dx$$

Parameters:

- p ([Distribution](/docs/generated/tensorplay.distributions.Distribution.html#tensorplay.distributions.Distribution)) – A [Distribution](/docs/generated/tensorplay.distributions.Distribution.html#tensorplay.distributions.Distribution) object.

- q ([Distribution](/docs/generated/tensorplay.distributions.Distribution.html#tensorplay.distributions.Distribution)) – A [Distribution](/docs/generated/tensorplay.distributions.Distribution.html#tensorplay.distributions.Distribution) object.

Returns:

A batch of KL divergences of shape batch_shape.

Return type:

[Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)

Raises:

[NotImplementedError](https://docs.python.org/3/builtins/exceptions.html#NotImplementedError) – If the distribution types have not been registered via
    [register_kl()](/docs/generated/tensorplay.distributions.register_kl.html#tensorplay.distributions.register_kl).

KL divergence is currently implemented for the following distribution pairs:

- [Bernoulli](/docs/generated/tensorplay.distributions.Bernoulli.html#tensorplay.distributions.Bernoulli) and [Bernoulli](/docs/generated/tensorplay.distributions.Bernoulli.html#tensorplay.distributions.Bernoulli)

- [Bernoulli](/docs/generated/tensorplay.distributions.Bernoulli.html#tensorplay.distributions.Bernoulli) and [Poisson](/docs/generated/tensorplay.distributions.Poisson.html#tensorplay.distributions.Poisson)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [Binomial](/docs/generated/tensorplay.distributions.Binomial.html#tensorplay.distributions.Binomial) and [Binomial](/docs/generated/tensorplay.distributions.Binomial.html#tensorplay.distributions.Binomial)

- [Categorical](/docs/generated/tensorplay.distributions.Categorical.html#tensorplay.distributions.Categorical) and [Categorical](/docs/generated/tensorplay.distributions.Categorical.html#tensorplay.distributions.Categorical)

- [Cauchy](/docs/generated/tensorplay.distributions.Cauchy.html#tensorplay.distributions.Cauchy) and [Cauchy](/docs/generated/tensorplay.distributions.Cauchy.html#tensorplay.distributions.Cauchy)

- [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [Dirichlet](/docs/generated/tensorplay.distributions.Dirichlet.html#tensorplay.distributions.Dirichlet) and [Dirichlet](/docs/generated/tensorplay.distributions.Dirichlet.html#tensorplay.distributions.Dirichlet)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [ExponentialFamily](/docs/generated/tensorplay.distributions.ExponentialFamily.html#tensorplay.distributions.ExponentialFamily) and [ExponentialFamily](/docs/generated/tensorplay.distributions.ExponentialFamily.html#tensorplay.distributions.ExponentialFamily)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [Geometric](/docs/generated/tensorplay.distributions.Geometric.html#tensorplay.distributions.Geometric) and [Geometric](/docs/generated/tensorplay.distributions.Geometric.html#tensorplay.distributions.Geometric)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [HalfNormal](/docs/generated/tensorplay.distributions.HalfNormal.html#tensorplay.distributions.HalfNormal) and [HalfNormal](/docs/generated/tensorplay.distributions.HalfNormal.html#tensorplay.distributions.HalfNormal)

- [Independent](/docs/generated/tensorplay.distributions.Independent.html#tensorplay.distributions.Independent) and [Independent](/docs/generated/tensorplay.distributions.Independent.html#tensorplay.distributions.Independent)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [LowRankMultivariateNormal](/docs/generated/tensorplay.distributions.LowRankMultivariateNormal.html#tensorplay.distributions.LowRankMultivariateNormal) and [LowRankMultivariateNormal](/docs/generated/tensorplay.distributions.LowRankMultivariateNormal.html#tensorplay.distributions.LowRankMultivariateNormal)

- [LowRankMultivariateNormal](/docs/generated/tensorplay.distributions.LowRankMultivariateNormal.html#tensorplay.distributions.LowRankMultivariateNormal) and [MultivariateNormal](/docs/generated/tensorplay.distributions.MultivariateNormal.html#tensorplay.distributions.MultivariateNormal)

- [MultivariateNormal](/docs/generated/tensorplay.distributions.MultivariateNormal.html#tensorplay.distributions.MultivariateNormal) and [LowRankMultivariateNormal](/docs/generated/tensorplay.distributions.LowRankMultivariateNormal.html#tensorplay.distributions.LowRankMultivariateNormal)

- [MultivariateNormal](/docs/generated/tensorplay.distributions.MultivariateNormal.html#tensorplay.distributions.MultivariateNormal) and [MultivariateNormal](/docs/generated/tensorplay.distributions.MultivariateNormal.html#tensorplay.distributions.MultivariateNormal)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Laplace](/docs/generated/tensorplay.distributions.Laplace.html#tensorplay.distributions.Laplace)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [OneHotCategorical](/docs/generated/tensorplay.distributions.OneHotCategorical.html#tensorplay.distributions.OneHotCategorical) and [OneHotCategorical](/docs/generated/tensorplay.distributions.OneHotCategorical.html#tensorplay.distributions.OneHotCategorical)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)

- [Poisson](/docs/generated/tensorplay.distributions.Poisson.html#tensorplay.distributions.Poisson) and [Bernoulli](/docs/generated/tensorplay.distributions.Bernoulli.html#tensorplay.distributions.Bernoulli)

- [Poisson](/docs/generated/tensorplay.distributions.Poisson.html#tensorplay.distributions.Poisson) and [Binomial](/docs/generated/tensorplay.distributions.Binomial.html#tensorplay.distributions.Binomial)

- [Poisson](/docs/generated/tensorplay.distributions.Poisson.html#tensorplay.distributions.Poisson) and [Poisson](/docs/generated/tensorplay.distributions.Poisson.html#tensorplay.distributions.Poisson)

- [TransformedDistribution](/docs/generated/tensorplay.distributions.TransformedDistribution.html#tensorplay.distributions.TransformedDistribution) and [TransformedDistribution](/docs/generated/tensorplay.distributions.TransformedDistribution.html#tensorplay.distributions.TransformedDistribution)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Beta](/docs/generated/tensorplay.distributions.Beta.html#tensorplay.distributions.Beta)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [ContinuousBernoulli](/docs/generated/tensorplay.distributions.ContinuousBernoulli.html#tensorplay.distributions.ContinuousBernoulli)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Exponential](/docs/generated/tensorplay.distributions.Exponential.html#tensorplay.distributions.Exponential)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Gamma](/docs/generated/tensorplay.distributions.Gamma.html#tensorplay.distributions.Gamma)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Normal](/docs/generated/tensorplay.distributions.Normal.html#tensorplay.distributions.Normal)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto)

- [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform) and [Uniform](/docs/generated/tensorplay.distributions.Uniform.html#tensorplay.distributions.Uniform)