def sample_heun(
    denoiser,
    x,
    sigmas,
    progress=False,
    s_churn=0.0,
    s_tmin=0.0,
    s_tmax=float("inf"),
    s_noise=1.0,
):
    """Implements Algorithm 2 (Heun steps) from Karras et al. (2022)."""
    s_in = x.new_ones([x.shape[0]])
    indices = range(len(sigmas) - 1)
    if progress:
        from tqdm.auto import tqdm

        indices = tqdm(indices)

    for i in indices:
        gamma = (
            min(s_churn / (len(sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.0
        )
        eps = th.randn_like(x) * s_noise
        sigma_hat = sigmas[i] * (gamma + 1)
        if gamma > 0:
            x = x + eps * (sigma_hat**2 - sigmas[i] ** 2) ** 0.5
        denoised = denoiser(x, sigma_hat * s_in)
        d = to_d(x, sigma_hat, denoised)
        yield {"x": x, "i": i, "sigma": sigmas[i], "sigma_hat": sigma_hat, "pred_xstart": denoised}
        dt = sigmas[i + 1] - sigma_hat
        if sigmas[i + 1] == 0:
            # Euler method
            x = x + d * dt
        else:
            # Heun's method
            x_2 = x + d * dt
            denoised_2 = denoiser(x_2, sigmas[i + 1] * s_in)
            d_2 = to_d(x_2, sigmas[i + 1], denoised_2)
            d_prime = (d + d_2) / 2
            x = x + d_prime * dt
    yield {"x": x, "pred_xstart": denoised}
Implements Algorithm 2 (Heun steps) from Karras et al. (2022).
shap_e/diffusion/k_diffusion.py