feat: adapt res samplers for flow models for eta > 0

[wbruna]

This adjusts the noise addition steps to follow the flow math. I believe the deterministic steps do not need further changes, apart from the sigma_up and sigma_down values.

@rmatif , could you please take a look?

[clort81]

I'm confused: existing get_ancestral_step is this:

    static std::pair<float, float> get_ancestral_step(float sigma_from, float sigma_to, float eta = 1.0f) {
    float sigma_up   = 0.0f;
    float sigma_down = sigma_to;
            
    if (eta <= 0.0f) {
        return {sigma_down, sigma_up};
    }   
    
    float sigma_from_sq = sigma_from * sigma_from;
    float sigma_to_sq   = sigma_to * sigma_to;
    if (sigma_from_sq > 0.0f) {
        float term = sigma_to_sq * (sigma_from_sq - sigma_to_sq) / sigma_from_sq;
        sigma_up   = std::min(sigma_to, eta * std::sqrt(std::max(term, 0.0f)));
    }   
    
    float sigma_down_sq = sigma_to_sq - sigma_up * sigma_up;
    sigma_down          = sigma_down_sq > 0.0f ? std::sqrt(sigma_down_sq) : 0.0f;
    return {sigma_down, sigma_up};
}

Does your pull request upgrade this function?

[wbruna]

Does your pull request upgrade this function?

Kind of: when running a flow model, it switches the samplers to use the similar get_ancestral_step_flow, and apply the additional signal scale. It's the same change that was done in #1374 for Euler Ancestral.

Note that eta=0 produces the same results on the two variants, and it's the default for these samplers, so you'll only notice a difference if you change it:

eta	master	PR
0.0
1.0