✨ (BetaSchedules) add Exponential schedule, from god knows where wth

docs/src/beta_schedules.md

@@ -9,11 +9,13 @@ T = 1000
 β_scaled_linear = scaled_linear_beta_schedule(T)
 β_cosine = cosine_beta_schedule(T)
 β_sigmoid = sigmoid_beta_schedule(T)
+β_exponential = exponential_beta_schedule(T)
 
 α̅_linear = cumprod(1 .- β_linear)
 α̅_scaled_linear = cumprod(1 .- β_scaled_linear)
 α̅_cosine = cumprod(1 .- β_cosine)
 α̅_sigmoid = cumprod(1 .- β_sigmoid)
+α̅_exponential = cumprod(1 .- β_exponential)
 
 p1 = plot(
   [
@@ -21,6 +23,7 @@ p1 = plot(
     scatter(y=β_scaled_linear, name="Scaled linear", visible="legendonly"),
     scatter(y=β_cosine, name="Cosine"),
     scatter(y=β_sigmoid, name="Sigmoid", visible="legendonly"),
+    scatter(y=β_exponential, name="Exponential", visible="legendonly"),
   ],
   Layout(
     updatemenus=[
@@ -57,6 +60,7 @@ p2 = plot(
     scatter(y=α̅_scaled_linear, name="Scaled linear", visible="legendonly"),
     scatter(y=α̅_cosine, name="Cosine"),
     scatter(y=α̅_sigmoid, name="Sigmoid", visible="legendonly"),
+    scatter(y=α̅_exponential, name="Exponential", visible="legendonly"),
   ],
   Layout(
     updatemenus=[
@@ -96,7 +100,6 @@ nothing
 <object type="text/html" data="alpha_bar_schedules.html" style="width:100%;height:420px;"></object>
 ```
 
-
 ```@autodocs
 Modules = [Diffusers.BetaSchedules]
 ```

src/BetaSchedules/BetaSchedules.jl

@@ -5,6 +5,7 @@ include("Linear.jl")
 include("ScaledLinear.jl")
 include("Cosine.jl")
 include("Sigmoid.jl")
+include("Exponential.jl")
 
 # utils
 include("ZeroSNR.jl")
@@ -15,6 +16,7 @@ export
   scaled_linear_beta_schedule,
   cosine_beta_schedule,
   sigmoid_beta_schedule,
+  exponential_beta_schedule,
 
   # Beta Schedule utils
   rescale_zero_terminal_snr

src/BetaSchedules/Exponential.jl

@@ -0,0 +1,27 @@
+"""
+Exponential beta schedule.
+
+## Input
+  * `T::Int`: number of timesteps
+  * `βₘₐₓ::Real=0.999f0`: maximum value of β
+
+## Output
+  * `β::Vector{Real}`: βₜ values at each timestep t
+
+## References
+"""
+function exponential_beta_schedule(T::Integer, βₘₐₓ::Real=0.999f0)
+  α̅(t) = exp(-12 * t / T)
+
+  β = Vector{Real}(undef, T)
+  for t in 1:T
+    αₜ = α̅(t) / α̅(t - 1)
+
+    βₜ = 1 - αₜ
+    βₜ = min(βₘₐₓ, βₜ)
+
+    β[t] = βₜ
+  end
+
+  return β
+end

src/Diffusers.jl

@@ -8,6 +8,7 @@ import .BetaSchedules:
   scaled_linear_beta_schedule,
   cosine_beta_schedule,
   sigmoid_beta_schedule,
+  exponential_beta_schedule,
 
   # Beta Schedule utils
   rescale_zero_terminal_snr
@@ -18,6 +19,7 @@ export
   scaled_linear_beta_schedule,
   cosine_beta_schedule,
   sigmoid_beta_schedule,
+  exponential_beta_schedule,
 
   # Beta Schedule utils
   rescale_zero_terminal_snr

src/Schedulers/DDPM.jl

@@ -32,13 +32,13 @@ struct DDPM{V<:AbstractVector} <: Scheduler
   β̅::V # 1 - α̅ (≠ cumprod(β))
 
   α̅₋₁::V # right-shifted α̅
-  β̅₋₁::V # 1 - α̅₋₁
+  β̅₋₁::V # right-shifted β̅
 
   ⎷α̅::V # square root of α̅
   ⎷β̅::V # square root of β̅
 
-  ⎷α̅₋₁::V # square root of α̅₋₁
-  ⎷β̅₋₁::V # square root of β̅₋₁
+  ⎷α̅₋₁::V # right-shifted ⎷α̅
+  ⎷β̅₋₁::V # right-shifted ⎷β̅
 end
 
 function DDPM(β::AbstractVector)