discretizer.py

from abc import abstractmethod
from functools import partial

import numpy as np
import torch

from ...modules.diffusionmodules.util import make_beta_schedule
from ...util import append_zero


def generate_roughly_equally_spaced_steps(
    num_substeps: int, max_step: int
) -> np.ndarray:
    return np.linspace(max_step - 1, 0, num_substeps, endpoint=False).astype(int)[::-1]

def sub_generate_roughly_equally_spaced_steps(
    num_substeps_1: int, num_substeps_2: int, max_step: int
) -> np.ndarray:
    substeps_2 = np.linspace(max_step - 1, 0, num_substeps_2, endpoint=False).astype(int)[::-1]
    substeps_1 = np.linspace(num_substeps_2 - 1, 0, num_substeps_1, endpoint=False).astype(int)[::-1]
    return substeps_2[substeps_1]

class Discretization:
    def __call__(self, n, do_append_zero=True, device="cpu", flip=False):
        sigmas = self.get_sigmas(n, device=device)
        sigmas = append_zero(sigmas) if do_append_zero else sigmas
        return sigmas if not flip else torch.flip(sigmas, (0,))

    @abstractmethod
    def get_sigmas(self, n, device):
        pass


class EDMDiscretization(Discretization):
    def __init__(self, sigma_min=0.002, sigma_max=80.0, rho=7.0):
        self.sigma_min = sigma_min
        self.sigma_max = sigma_max
        self.rho = rho

    def get_sigmas(self, n, device="cpu"):
        ramp = torch.linspace(0, 1, n, device=device)
        min_inv_rho = self.sigma_min ** (1 / self.rho)
        max_inv_rho = self.sigma_max ** (1 / self.rho)
        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** self.rho
        return sigmas


class LegacyDDPMDiscretization(Discretization):
    def __init__(
        self,
        linear_start=0.00085,
        linear_end=0.0120,
        num_timesteps=1000,
    ):
        super().__init__()
        self.num_timesteps = num_timesteps
        betas = make_beta_schedule(
            "linear", num_timesteps, linear_start=linear_start, linear_end=linear_end
        )
        alphas = 1.0 - betas
        self.alphas_cumprod = np.cumprod(alphas, axis=0)
        self.to_torch = partial(torch.tensor, dtype=torch.float32)

    def get_sigmas(self, n, device="cpu"):
        if n < self.num_timesteps:
            timesteps = generate_roughly_equally_spaced_steps(n, self.num_timesteps)
            alphas_cumprod = self.alphas_cumprod[timesteps]
        elif n == self.num_timesteps:
            alphas_cumprod = self.alphas_cumprod
        else:
            raise ValueError

        to_torch = partial(torch.tensor, dtype=torch.float32, device=device)
        sigmas = to_torch((1 - alphas_cumprod) / alphas_cumprod) ** 0.5
        return torch.flip(sigmas, (0,)) # sigma_t: 14.4 -> 0.029

class ZeroSNRDDPMDiscretization(Discretization):
    def __init__(
        self,
        linear_start=0.00085,
        linear_end=0.0120,
        num_timesteps=1000,
        shift_scale=1.,
    ):
        super().__init__()
        self.num_timesteps = num_timesteps
        betas = make_beta_schedule(
            "linear", num_timesteps, linear_start=linear_start, linear_end=linear_end
        )
        alphas = 1.0 - betas
        self.alphas_cumprod = np.cumprod(alphas, axis=0)
        self.to_torch = partial(torch.tensor, dtype=torch.float32)

        self.alphas_cumprod = self.alphas_cumprod / (shift_scale + (1-shift_scale) * self.alphas_cumprod)

    def get_sigmas(self, n, device="cpu", return_idx=False):
        if n < self.num_timesteps:
            timesteps = generate_roughly_equally_spaced_steps(n, self.num_timesteps)
            alphas_cumprod = self.alphas_cumprod[timesteps]
        elif n == self.num_timesteps:
            alphas_cumprod = self.alphas_cumprod
        else:
            raise ValueError

        to_torch = partial(torch.tensor, dtype=torch.float32, device=device)
        alphas_cumprod = to_torch(alphas_cumprod)
        alphas_cumprod_sqrt = alphas_cumprod.sqrt()
        alphas_cumprod_sqrt_0 = alphas_cumprod_sqrt[0].clone()
        alphas_cumprod_sqrt_T = alphas_cumprod_sqrt[-1].clone()

        alphas_cumprod_sqrt -= alphas_cumprod_sqrt_T
        alphas_cumprod_sqrt *= alphas_cumprod_sqrt_0 / (alphas_cumprod_sqrt_0 - alphas_cumprod_sqrt_T)

        if return_idx:
            return torch.flip(alphas_cumprod_sqrt, (0,)), timesteps
        else:
            return torch.flip(alphas_cumprod_sqrt, (0,)) # sqrt(alpha_t): 0 -> 0.99
        
    def __call__(self, n, do_append_zero=True, device="cpu", flip=False, return_idx=False):
        if return_idx:
            sigmas, idx = self.get_sigmas(n, device=device, return_idx=True)
            sigmas = append_zero(sigmas) if do_append_zero else sigmas
            return (sigmas, idx) if not flip else (torch.flip(sigmas, (0,)), torch.flip(idx, (0,)))
        else:
            sigmas = self.get_sigmas(n, device=device)
            sigmas = append_zero(sigmas) if do_append_zero else sigmas
            return sigmas if not flip else torch.flip(sigmas, (0,))