class

VPSDE

extendsSDE

VPSDE(beta_min: float = 0.1, beta_max: float = 20.0)

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Variance Preserving — the continuous limit of DDPM.

Parameters

beta_minfloat= 0.1

The linear rate range. The paper's values, "to match the settings in Ho et al. (2020)".

beta_maxfloat= 0.1

The linear rate range. The paper's values, "to match the settings in Ho et al. (2020)".

Notes

Song et al. (2021), equation 32:

dx = -\tfrac{1}{2}\big(\bar\beta_{\min} + t(\bar\beta_{\max} - \bar\beta_{\min})\big) x\, dt + \sqrt{\bar\beta_{\min} + t(\bar\beta_{\max} - \bar\beta_{\min})}\; dw,

with the perturbation kernel of equation 33. Starting from unit variance the process keeps it, which is the difference from VE and the reason the prior is a standard normal rather than a wide one.

Examples

>>> from lucid.models.generative.score_sde._sde import VPSDE
>>> sde = VPSDE(beta_min=0.1, beta_max=20.0)
>>> sde.prior_variance
1.0
Variance preserving: the process is scaled so the terminal
distribution is the unit Gaussian, which is the same place DDPM
ends up and why the two are usually interchangeable.

Used by 1

lucid.models.generative.score_sde

Constructors

dunder

init

→None

__init__(beta_min: float = 0.1, beta_max: float = 20.0)

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Initialise the SDE. See the class docstring for parameters.

Properties

prop

prior_variance

→float

prior_variance: float

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One — the process is variance preserving.

prop

t_min

→float

t_min: float

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The paper's sampling epsilon, chosen so the variance matches DDPM's.

Instance methods

beta

→Tensor

beta(t: Tensor)

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$\beta(t) = \bar\beta_{\min} + t(\bar\beta_{\max} - \bar\beta_{\min})$ .

diffusion

→Tensor

diffusion(t: Tensor)

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$\sqrt{\beta(t)}$ .

drift

→Tensor

drift(x: Tensor, t: Tensor)

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$-\tfrac{1}{2}\beta(t)x$ .

marginal_prob

→tuple[Tensor, Tensor]

marginal_prob(x: Tensor, t: Tensor)

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Equation 33.

prior_sampling

→Tensor

prior_sampling(shape: tuple[int, ...], device: str)

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$\mathcal{N}(0, I)$ .

>>> from lucid.models.generative.score_sde._sde import VPSDE >>> sde = VPSDE(beta_min=0.1, beta_max=20.0) >>> sde.prior_variance 1.0 Variance preserving: the process is scaled so the terminal distribution is the unit Gaussian, which is the same place DDPM ends up and why the two are usually interchangeable.