diff --git a/src/DDPM.jl b/src/DDPM.jl
index 826b6a8..be491cf 100644
--- a/src/DDPM.jl
+++ b/src/DDPM.jl
@@ -3,34 +3,35 @@ include("Schedulers.jl")
 """
 Denoising Diffusion Probabilistic Models (DDPM) scheduler.
 
-cf. [[2006.11239] Denoising Diffusion Probabilistic Models](https://arxiv.org/abs/2006).
+cf. [[2006.11239] Denoising Diffusion Probabilistic Models](https://arxiv.org/abs/2006.11239)
 """
 struct DDPM{V<:AbstractVector} <: Scheduler
   # number of diffusion steps used to train the model.
-  num_train_timesteps::Int
+  T_train::Int
 
-  # the betas to use for the diffusion steps
-  βs::V
-  αs::V
+  # the betas used for the diffusion steps
+  β::V
+
+  # internal variables used for computation (derived from β)
+  α::V
   α_cumprods::V
   α_cumprod_prevs::V
-
   sqrt_α_cumprods::V
   sqrt_one_minus_α_cumprods::V
 end
 
-function DDPM(V::DataType, βs::AbstractVector)
-  αs = 1 .- βs
-  α_cumprods = cumprod(αs)
+function DDPM(V::DataType, β::AbstractVector)
+  α = 1 .- β
+  α_cumprods = cumprod(α)
   α_cumprod_prevs = [1, (α_cumprods[1:end-1])...]
 
   sqrt_α_cumprods = sqrt.(α_cumprods)
   sqrt_one_minus_α_cumprods = sqrt.(1 .- α_cumprods)
 
   DDPM{V}(
-    length(βs),
-    βs,
-    αs,
+    length(β),
+    β,
+    α,
     α_cumprods,
     α_cumprod_prevs,
     sqrt_α_cumprods,
@@ -81,7 +82,7 @@ function step(
   pred_prev_sample = pred_original_sample_coeff' .* x_0_pred + current_sample_coeff' .* sample
 
   # 6. Add noise
-  variance = sqrt.(scheduler.βs[timesteps])' .* randn(size(model_output))
+  variance = sqrt.(scheduler.β[timesteps])' .* randn(size(model_output))
   pred_prev_sample = pred_prev_sample + variance
 
   return pred_prev_sample, x_0_pred
diff --git a/src/Schedulers.jl b/src/Schedulers.jl
index 6c7a5f2..707d21f 100644
--- a/src/Schedulers.jl
+++ b/src/Schedulers.jl
@@ -3,6 +3,8 @@ abstract type Scheduler end
 """
 Add noise to clean data using the forward diffusion process.
 
+cf. [[2006.11239] Denoising Diffusion Probabilistic Models](https://arxiv.org/abs/2006.11239) (Eq. 4)
+
 ## Input
   * scheduler (`Scheduler`): scheduler to use
   * clean_data (`AbstractArray`): clean data to add noise to