class

TransformedDistribution

extendsDistribution

TransformedDistribution(base_distribution: Distribution, transforms: Transform | list[Transform], validate_args: bool | None = None)

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Pushforward of a base distribution through a (composite) bijector.

Constructs a new Distribution whose samples are obtained by pushing samples from base_distribution through the supplied chain of Transform instances, with log_prob accounting for the Jacobian correction via the change-of-variable formula. This is the canonical way to build normalising flows in Lucid: stack any number of bijections on top of a tractable base (typically a Normal) to obtain expressive densities while retaining exact log-likelihood evaluation and reparameterised sampling.

Parameters

base_distributionDistribution

Underlying distribution whose samples will be pushed through transforms.

transformsTransform or list[Transform]

A single transform or an ordered list applied left-to-right. Internally wrapped in a list.

validate_argsbool= None

Forwarded to Distribution.

Notes

Sampling (with $T = T_n \circ \cdots \circ T_1$ the composite bijector):

Y = T(X), \quad X \sim p_{\text{base}}

Reparameterised sampling is available iff the base distribution supports it (has_rsample is forwarded).

Density (change of variables):

\log p_Y(\mathbf{y}) = \log p_X(T^{-1}(\mathbf{y})) - \sum_{i=1}^{n} \log\!\left|\det \frac{\partial T_i(\mathbf{x}_{i-1})}{\partial \mathbf{x}_{i-1}}\right|

where $\mathbf{x}_0 = T^{-1}(\mathbf{y})$ and $\mathbf{x}_i = T_i(\mathbf{x}_{i-1})$ . The implementation walks the transforms in reverse, inverting one step at a time and accumulating the Jacobian correction.

Examples

>>> import lucid
>>> from lucid.distributions import Normal
>>> from lucid.distributions.transforms import (
...     ExpTransform, TransformedDistribution)
>>> # LogNormal = ExpTransform(Normal(0, 1))
>>> log_normal = TransformedDistribution(Normal(loc=0.0, scale=1.0), [ExpTransform()])
>>> log_normal.rsample((4,))
Tensor([...])
>>> log_normal.log_prob(lucid.tensor(1.0))
Tensor(...)

Used by 1

lucid.distributions

Constructors

dunder

init

→None

__init__(base_distribution: Distribution, transforms: Transform | list[Transform], validate_args: bool | None = None)

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Construct a transformed distribution.

Parameters

base_distributionDistribution

Underlying distribution whose samples will be pushed through transforms.

transformsTransform | list[Transform]

A single transform or an ordered list applied left-to-right.

validate_argsbool | None= None

Forwarded to Distribution.

Properties

prop

has_rsample

→bool

has_rsample: bool

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Whether reparameterised sampling is available — inherited from the base distribution.

Instance methods

log_prob

→Tensor

log_prob(value: Tensor)

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Evaluate the log-density of value under the transformed distribution.

Uses the change-of-variable formula:

\log p(y) = \log p_{\text{base}}(T^{-1}(y)) - \sum_i \log\!\bigl|\det \partial T_i / \partial x_i\bigr|

with the chain unwound by walking the transforms in reverse.

rsample

→Tensor

rsample(sample_shape: tuple[int, ...] = ())

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Push a reparameterised base sample through the transform chain.

sample

→Tensor

sample(sample_shape: tuple[int, ...] = ())

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Push a (non-reparameterised) base sample through the transform chain.

>>> import lucid >>> from lucid.distributions import Normal >>> from lucid.distributions.transforms import ( ... ExpTransform, TransformedDistribution) >>> # LogNormal = ExpTransform(Normal(0, 1)) >>> log_normal = TransformedDistribution(Normal(loc=0.0, scale=1.0), [ExpTransform()]) >>> log_normal.rsample((4,)) Tensor([...]) >>> log_normal.log_prob(lucid.tensor(1.0)) Tensor(...)