✨ (BetaSchedulers) add rescale_zero_terminal_snr

src/BetaSchedulers.jl

@@ -11,7 +11,7 @@ cf. [[2006.11239] Denoising Diffusion Probabilistic Models](https://arxiv.org/ab
   * β_T (`Real := 0.02f0`): final value of β
 
 ## Output
-  * βs (`Vector{Real}`): β_t values at each timestep t
+  * β (`Vector{Real}`): β_t values at each timestep t
 """
 function linear_beta_schedule(T::Int, β_1::Real=0.0001f0, β_T::Real=0.02f0)
   return range(start=β_1, stop=β_T, length=T)
@@ -28,7 +28,7 @@ cf. [[2006.11239] Denoising Diffusion Probabilistic Models](https://arxiv.org/ab
   * β_T (`Real := 0.02f0`): final value of β
 
 ## Output
-  * βs (`Vector{Real}`): β_t values at each timestep t
+  * β (`Vector{Real}`): β_t values at each timestep t
 """
 function scaled_linear_beta_schedule(T::Int, β_1::Real=0.0001f0, β_T::Real=0.02f0)
   return range(start=β_1^0.5, stop=β_T^0.5, length=T) .^ 2
@@ -46,11 +46,11 @@ and [github.com:MinkaiXu/GeoDiff](https://github.com/MinkaiXu/GeoDiff/blob/ea0ca
   * β_T (`Real := 0.02f0`): final value of β
 
 ## Output
-  * βs (`Vector{Real}`): β_t values at each timestep t
+  * β (`Vector{Real}`): β_t values at each timestep t
 """
 function sigmoid_beta_schedule(T::Int, β_1::Real=0.0001f0, β_T::Real=0.02f0)
   x = range(start=-6, stop=6, length=T)
-  return sigmoid(x) * (β_T - β_1) + β_1
+  return sigmoid(x) .* (β_T - β_1) .+ β_1
 end
 
 """
@@ -64,12 +64,12 @@ cf. [[2102.09672] Improved Denoising Diffusion Probabilistic Models](https://arx
   * ϵ (`Real := 1e-3f0`): small value used to avoid division by zero
 
 ## Output
-  * βs (`Vector{Real}`): β_t values at each timestep t
+  * β (`Vector{Real}`): β_t values at each timestep t
 """
-function cosine_beta_schedule(T::Int, β_max::Real=0.999f0, ϵ::Real=1e-3f0)
+function cosine_beta_schedule(T::Int, β_max::Real=0.999f0, ϵ::Real=0.001f0)
   α_bar(t) = cos((t + ϵ) / (1 + ϵ) * π / 2)^2
 
-  βs = Float32[]
+  β = Float32[]
   for t in 1:T
     t1 = (t - 1) / T
     t2 = t / T
@@ -77,8 +77,44 @@ function cosine_beta_schedule(T::Int, β_max::Real=0.999f0, ϵ::Real=1e-3f0)
     β_t = 1 - α_bar(t2) / α_bar(t1)
     β_t = min(β_max, β_t)
 
-    push!(βs, β_t)
+    push!(β, β_t)
   end
 
-  return βs
+  return β
+end
+
+"""
+Rescale betas to have zero terminal SNR.
+
+cf. [[2305.08891] Rescaling Diffusion Models](https://arxiv.org/abs/2305.08891) (Algorithm 1)
+
+## Input
+  * β (`AbstractArray`): β_t values at each timestep t
+
+## Output
+  * β (`Vector{Real}`): rescaled β_t values at each timestep t
+"""
+function rescale_zero_terminal_snr(β::AbstractArray)
+  # convert β to sqrt_α_cumprods
+  α = 1 .- β
+  α_cumprod = cumprod(α)
+  sqrt_α_cumprods = sqrt.(α_cumprod)
+
+  # store old extrema values
+  sqrt_α_cumprod_1 = sqrt_α_cumprods[1]
+  sqrt_α_cumprod_T = sqrt_α_cumprods[end]
+
+  # shift last timestep to zero
+  sqrt_α_cumprods .-= sqrt_α_cumprod_T
+
+  # scale so that first timestep reaches old values
+  sqrt_α_cumprods *= sqrt_α_cumprod_1 / (sqrt_α_cumprod_1 - sqrt_α_cumprod_T)
+
+  # convert back sqrt_α_cumprods to β
+  α_cumprod = sqrt_α_cumprods .^ 2
+  α = α_cumprod[2:end] ./ α_cumprod[1:end-1]
+  α = vcat(α_cumprod[1], α)
+  β = 1 .- α
+
+  return β
 end