priorschedule

Prior schedule functions for DDPM diffusion models.

This module defines a base abstract class for prior schedules and two common concrete implementations:

• LinearPriorSchedule: \(\alpha(t) = t\)
• QuadraticPriorSchedule: \(\alpha(t) = t^2\)

Classes:

• PriorSchedule –

  Abstract base for defining \(\alpha(t)\) schedules.

• LinearPriorSchedule –

  Simple linear schedule.

• QuadraticPriorSchedule –

  Simple quadratic schedule.

Notes

It is assumed that the time steps t are normalized to the range [0, 1].

PriorSchedule

Bases: ABC

Abstract base class for prior schedules in DDPM models.

A prior schedule defines the mixing coefficient \(\alpha(t)\) that controls how the model incorporates the prior distribution over time steps in a diffusion process.

Methods:

• alpha –

  Compute the schedule coefficient \(\alpha\) at time \(t\).

alpha(t) abstractmethod

Compute the schedule coefficient \(\alpha\) at time \(t\).

Parameters:

• t ((array_like, shape(dim1))) –

  Time steps \(t\in[0, 1]\).

Returns:

• alpha_t ( (array_like, shape(dim1)) ) –

  Mixing coefficients corresponding to each time in \(t\).

Source code in src/fpsl/ddm/priorschedule.py

@abstractmethod
def alpha(self, t: Float[ArrayLike, ' dim1']) -> Float[ArrayLike, ' dim1']:
    r"""Compute the schedule coefficient $\alpha$ at time $t$.

    Parameters
    ----------
    t : array_like, shape (dim1,)
        Time steps $t\in[0, 1]$.

    Returns
    -------
    alpha_t : array_like, shape (dim1,)
        Mixing coefficients corresponding to each time in $t$.
    """
    raise NotImplementedError

LinearPriorSchedule

Bases: PriorSchedule

Linearly increasing prior schedule.

\(\alpha(t) = t\)

Methods:

• alpha –

  Compute the schedule coefficient \(\alpha\) at time \(t\).

alpha(t)

Linear schedule function.

Parameters:

• t ((array_like, shape(dim1))) –

  Time steps \(t\in[0, 1]\).

Returns:

• alpha_t ( (array_like, shape(dim1)) ) –

  Equal to the input t.

Source code in src/fpsl/ddm/priorschedule.py

def alpha(self, t: Float[ArrayLike, ' dim1']) -> Float[ArrayLike, ' dim1']:
    r"""Linear schedule function.

    Parameters
    ----------
    t : array_like, shape (dim1,)
        Time steps $t\in[0, 1]$.

    Returns
    -------
    alpha_t : array_like, shape (dim1,)
        Equal to the input t.
    """
    return t

QuadraticPriorSchedule

Bases: PriorSchedule

Quadratically increasing prior schedule \(\alpha(t) = t^2\).

Methods:

• alpha –

  Compute the schedule coefficient \(\alpha\) at time \(t\).

alpha(t)

Quadratic schedule function.

Parameters:

• t ((array_like, shape(dim1))) –

  Time steps \(t\in[0, 1]\).

Returns:

• alpha_t ( (array_like, shape(dim1)) ) –

  Squares of the input t.

Source code in src/fpsl/ddm/priorschedule.py

def alpha(self, t: Float[ArrayLike, ' dim1']) -> Float[ArrayLike, ' dim1']:
    r"""Quadratic schedule function.

    Parameters
    ----------
    t : array_like, shape (dim1,)
        Time steps $t\in[0, 1]$.

    Returns
    -------
    alpha_t : array_like, shape (dim1,)
        Squares of the input t.
    """
    return t**2