diff --git a/src/multivariate.jl b/src/multivariate.jl
index 225823a7..29bf2358 100644
--- a/src/multivariate.jl
+++ b/src/multivariate.jl
@@ -103,6 +103,12 @@ function MvNormal(
 )
     return TuringMvNormal(m, D)
 end
+function MvNormal(
+    m::TrackedVector{<:Real},
+    D::Diagonal{T, <:AbstractVector{T}} where {T<:Real},
+)
+    return TuringMvNormal(m, D)
+end
 
 # dense mean, diagonal covariance
 MvNormal(m::TrackedVector{<:Real}, σ::TrackedVector{<:Real}) = TuringMvNormal(m, σ)
@@ -211,6 +217,18 @@ function MvLogNormal(
 )
     return TuringMvLogNormal(TuringMvNormal(m, D))
 end
+function MvLogNormal(
+    m::TrackedVector{<:Real},
+    D::Diagonal{T, <:AbstractVector{T}} where {T<:Real},
+)
+    return TuringMvLogNormal(TuringMvNormal(m, D))
+end
+function MvLogNormal(
+    m::AbstractVector{<:Real},
+    D::Diagonal{T, <:AbstractVector{T}} where {T<:Real},
+)
+    return MvLogNormal(MvNormal(m, D))
+end
 
 # dense mean, diagonal covariance
 MvLogNormal(m::TrackedVector{<:Real}, σ::TrackedVector{<:Real}) = TuringMvLogNormal(TuringMvNormal(m, σ))
diff --git a/test/distributions.jl b/test/distributions.jl
index 4071222d..450c689f 100644
--- a/test/distributions.jl
+++ b/test/distributions.jl
@@ -176,26 +176,34 @@ separator()
         # Vector case
         DistSpec(:MvNormal, (mean, cov_mat), norm_val_vec),
         DistSpec(:MvNormal, (mean, cov_vec), norm_val_vec),
+        DistSpec(:MvNormal, (mean, Diagonal(cov_vec)), norm_val_vec),
         DistSpec(:MvNormal, (mean, cov_num), norm_val_vec),
         DistSpec(:((m, v) -> MvNormal(m, v*I)), (mean, cov_num), norm_val_vec),
         DistSpec(:MvNormal, (cov_mat,), norm_val_vec),
         DistSpec(:MvNormal, (cov_vec,), norm_val_vec),
+        DistSpec(:MvNormal, (Diagonal(cov_vec),), norm_val_vec),
         DistSpec(:(cov_num -> MvNormal(dim, cov_num)), (cov_num,), norm_val_vec),
         DistSpec(:MvLogNormal, (mean, cov_mat), norm_val_vec),
         DistSpec(:MvLogNormal, (mean, cov_vec), norm_val_vec),
+        DistSpec(:MvLogNormal, (mean, Diagonal(cov_vec)), norm_val_vec),
         DistSpec(:MvLogNormal, (mean, cov_num), norm_val_vec),
         DistSpec(:MvLogNormal, (cov_mat,), norm_val_vec),
         DistSpec(:MvLogNormal, (cov_vec,), norm_val_vec),
+        DistSpec(:MvLogNormal, (Diagonal(cov_vec),), norm_val_vec),
         DistSpec(:(cov_num -> MvLogNormal(dim, cov_num)), (cov_num,), norm_val_vec),
         # Matrix case
         DistSpec(:MvNormal, (mean, cov_vec), norm_val_mat),
+        DistSpec(:MvNormal, (mean, Diagonal(cov_vec)), norm_val_mat),
         DistSpec(:MvNormal, (mean, cov_num), norm_val_mat),
         DistSpec(:((m, v) -> MvNormal(m, v*I)), (mean, cov_num), norm_val_mat),
         DistSpec(:MvNormal, (cov_vec,), norm_val_mat),
+        DistSpec(:MvNormal, (Diagonal(cov_vec),), norm_val_mat),
         DistSpec(:(cov_num -> MvNormal(dim, cov_num)), (cov_num,), norm_val_mat),
         DistSpec(:MvLogNormal, (mean, cov_vec), norm_val_mat),
+        DistSpec(:MvLogNormal, (mean, Diagonal(cov_vec)), norm_val_mat),
         DistSpec(:MvLogNormal, (mean, cov_num), norm_val_mat),
         DistSpec(:MvLogNormal, (cov_vec,), norm_val_mat),
+        DistSpec(:MvLogNormal, (Diagonal(cov_vec),), norm_val_mat),
         DistSpec(:(cov_num -> MvLogNormal(dim, cov_num)), (cov_num,), norm_val_mat),
     ]
 
diff --git a/test/test_utils.jl b/test/test_utils.jl
index 1f3f309b..add03f5f 100644
--- a/test/test_utils.jl
+++ b/test/test_utils.jl
@@ -10,6 +10,7 @@ struct DistSpec{Tθ<:Tuple, Tx}
 end
 
 vectorize(v::Number) = [v]
+vectorize(v::Diagonal) = v.diag
 vectorize(v) = vec(v)
 pack(vals...) = reduce(vcat, vectorize.(vals))
 @generated function unpack(x, vals...)
@@ -22,6 +23,9 @@ pack(vals...) = reduce(vcat, vectorize.(vals))
         elseif T <: Vector
             push!(unpacked, :(x[$ind:$ind+length(vals[$i])-1]))
             ind = :($ind + length(vals[$i]))
+        elseif T <: Diagonal
+            push!(unpacked, :(Diagonal(x[$ind:$ind+size(vals[$i],1)-1])))
+            ind = :($ind + size(vals[$i],1))
         elseif T <: Matrix
             push!(unpacked, :(reshape(x[$ind:($ind+length(vals[$i])-1)], size(vals[$i]))))
             ind = :($ind + length(vals[$i]))