Project reverse-diffusion helper

Read the equation

The code subtracts √(1−α) times its predicted noise, divides by √α, and adds σ times fresh noise. It requires 0<α≤1. Under the usual DDPM noise-prediction convention, the reverse mean instead uses (1−αₜ)/√(1−ᾱₜ) as the predicted-noise coefficient; this helper lacks ᾱ and should be described as its own update unless the caller supplies a correspondingly rescaled prediction.

Terms & definitions

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Original context

		}
		result[i] = sqrtAlpha*x0[i] + sqrtOneMinusAlpha*n
	}
	return result
}

// ReverseDiffusion computes one step of reverse diffusion
// x_{t-1} = (x_t - √(1-α_t)ε_θ) / √α_t + σ_t z
func ReverseDiffusion(xt []float64, epsilonPred []float64, alpha, sigma float64, noise []float64) []float64 {
	sqrtAlpha := math.Sqrt(alpha)
	sqrtOneMinusAlpha := math.Sqrt(1.0 - alpha)

	result := make([]float64, len(xt))
	for i := range result {
		eps := 0.0
		if i < len(epsilonPred) {
			eps = epsilonPred[i]
		}

x_{t-1} = (x_t - √(1-α_t)ε_θ) / √α_t + σ_t z

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