diff --git a/Project.toml b/Project.toml
index 0fba3bc1..56a638c5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "DistributionsAD"
 uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
-version = "0.6.18"
+version = "0.6.19"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/multivariate.jl b/src/multivariate.jl
index 0f388ebb..634c023d 100644
--- a/src/multivariate.jl
+++ b/src/multivariate.jl
@@ -1,52 +1,54 @@
 ## Dirichlet ##
 
-struct TuringDirichlet{T, TV <: AbstractVector} <: ContinuousMultivariateDistribution
+struct TuringDirichlet{T<:Real,TV<:AbstractVector,S<:Real} <: ContinuousMultivariateDistribution
     alpha::TV
     alpha0::T
-    lmnB::T
-end
-Base.length(d::TuringDirichlet) = length(d.alpha)
-function check(alpha)
-    all(ai -> ai > 0, alpha) || 
-        throw(ArgumentError("Dirichlet: alpha must be a positive vector."))
-end
-
-function Distributions._rand!(rng::Random.AbstractRNG,
-                d::TuringDirichlet,
-                x::AbstractVector{<:Real})
-    s = 0.0
-    n = length(x)
-    α = d.alpha
-    for i in 1:n
-        @inbounds s += (x[i] = rand(rng, Gamma(α[i])))
-    end
-    Distributions.multiply!(x, inv(s)) # this returns x
+    lmnB::S
 end
 
 function TuringDirichlet(alpha::AbstractVector)
-    check(alpha)
+    all(ai -> ai > 0, alpha) ||
+        throw(ArgumentError("Dirichlet: alpha must be a positive vector."))
+
     alpha0 = sum(alpha)
     lmnB = sum(loggamma, alpha) - loggamma(alpha0)
-    T = promote_type(typeof(alpha0), typeof(lmnB))
-    TV = typeof(alpha)
-    TuringDirichlet{T, TV}(alpha, alpha0, lmnB)
-end
 
-function TuringDirichlet(d::Integer, alpha::Real)
-    alpha0 = alpha * d
-    _alpha = fill(alpha, d)
-    lmnB = loggamma(alpha) * d - loggamma(alpha0)
-    T = promote_type(typeof(alpha0), typeof(lmnB))
-    TV = typeof(_alpha)
-    TuringDirichlet{T, TV}(_alpha, alpha0, lmnB)
-end
-function TuringDirichlet(alpha::AbstractVector{T}) where {T <: Integer}
-    TuringDirichlet(float.(alpha))
+    return TuringDirichlet(alpha, alpha0, lmnB)
 end
-TuringDirichlet(d::Integer, alpha::Integer) = TuringDirichlet(d, Float64(alpha))
+TuringDirichlet(d::Integer, alpha::Real) = TuringDirichlet(Fill(alpha, d))
 
+# TODO: remove?
+TuringDirichlet(alpha::AbstractVector{<:Integer}) = TuringDirichlet(float.(alpha))
+TuringDirichlet(d::Integer, alpha::Integer) = TuringDirichlet(d, float(alpha))
+
+# TODO: remove and use `Dirichlet` only for `Tracker.TrackedVector`
 Distributions.Dirichlet(alpha::AbstractVector) = TuringDirichlet(alpha)
 
+TuringDirichlet(d::Dirichlet) = TuringDirichlet(d.alpha, d.alpha0, d.lmnB)
+
+Base.length(d::TuringDirichlet) = length(d.alpha)
+
+# copied from Distributions
+# TODO: remove and use `Dirichlet`?
+function Distributions._rand!(
+    rng::Random.AbstractRNG,
+    d::TuringDirichlet,
+    x::AbstractVector{<:Real},
+)
+    @inbounds for (i, αi) in zip(eachindex(x), d.alpha)
+        x[i] = rand(rng, Gamma(αi))
+    end
+    Distributions.multiply!(x, inv(sum(x))) # this returns x
+end
+function Distributions._rand!(
+    rng::AbstractRNG,
+    d::TuringDirichlet{<:Real,<:FillArrays.AbstractFill},
+    x::AbstractVector{<:Real}
+)
+    rand!(rng, Gamma(FillArrays.getindex_value(d.alpha)), x)
+    Distributions.multiply!(x, inv(sum(x))) # this returns x
+end
+
 function Distributions._logpdf(d::TuringDirichlet, x::AbstractVector{<:Real})
     return simplex_logpdf(d.alpha, d.lmnB, x)
 end
diff --git a/src/reversediff.jl b/src/reversediff.jl
index a4c9f42b..6e853d3b 100644
--- a/src/reversediff.jl
+++ b/src/reversediff.jl
@@ -260,13 +260,13 @@ Dirichlet(alpha::AbstractVector{<:TrackedReal}) = TuringDirichlet(alpha)
 Dirichlet(d::Integer, alpha::TrackedReal) = TuringDirichlet(d, alpha)
 
 function _logpdf(d::Dirichlet, x::AbstractVector{<:TrackedReal})
-    return _logpdf(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+    return _logpdf(TuringDirichlet(d), x)
 end
 function logpdf(d::Dirichlet, x::AbstractMatrix{<:TrackedReal})
-    return logpdf(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+    return logpdf(TuringDirichlet(d), x)
 end
 function loglikelihood(d::Dirichlet, x::AbstractMatrix{<:TrackedReal})
-    return loglikelihood(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+    return loglikelihood(TuringDirichlet(d), x)
 end
 
 # default definition of `loglikelihood` yields gradients of zero?!
diff --git a/src/tracker.jl b/src/tracker.jl
index f08ec1ad..f4a79067 100644
--- a/src/tracker.jl
+++ b/src/tracker.jl
@@ -371,13 +371,13 @@ Distributions.Dirichlet(alpha::TrackedVector) = TuringDirichlet(alpha)
 Distributions.Dirichlet(d::Integer, alpha::TrackedReal) = TuringDirichlet(d, alpha)
 
 function Distributions._logpdf(d::Dirichlet, x::TrackedVector{<:Real})
-    return Distributions._logpdf(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+    return Distributions._logpdf(TuringDirichlet(d), x)
 end
 function Distributions.logpdf(d::Dirichlet, x::TrackedMatrix{<:Real})
-    return logpdf(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+    return logpdf(TuringDirichlet(d), x)
 end
 function Distributions.loglikelihood(d::Dirichlet, x::TrackedMatrix{<:Real})
-    return loglikelihood(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+    return loglikelihood(TuringDirichlet(d), x)
 end
 
 # Fix ambiguities
@@ -615,4 +615,3 @@ Distributions.InverseWishart(df::TrackedReal, S::AbstractMatrix{<:Real}) = Turin
 Distributions.InverseWishart(df::Real, S::TrackedMatrix) = TuringInverseWishart(df, S)
 Distributions.InverseWishart(df::TrackedReal, S::TrackedMatrix) = TuringInverseWishart(df, S)
 Distributions.InverseWishart(df::TrackedReal, S::AbstractPDMat{<:TrackedReal}) = TuringInverseWishart(df, S)
-
diff --git a/test/others.jl b/test/others.jl
index fc6308a4..fc545bfd 100644
--- a/test/others.jl
+++ b/test/others.jl
@@ -298,4 +298,42 @@
             end
         end
     end
+
+    @testset "TuringDirichlet" begin
+        dim = 3
+        n = 4
+        for alpha in (2, rand())
+            d1 = TuringDirichlet(dim, alpha)
+            d2 = Dirichlet(dim, alpha)
+            d3 = TuringDirichlet(d2)
+            @test d1.alpha == d2.alpha == d3.alpha
+            @test d1.alpha0 == d2.alpha0 == d3.alpha0
+            @test d1.lmnB == d2.lmnB == d3.lmnB
+
+            s1 = rand(d1)
+            @test s1 isa Vector{Float64}
+            @test length(s1) == dim
+
+            s2 = rand(d1, n)
+            @test s2 isa Matrix{Float64}
+            @test size(s2) == (dim, n)
+        end
+
+        for alpha in (ones(Int, dim), rand(dim))
+            d1 = TuringDirichlet(alpha)
+            d2 = Dirichlet(alpha)
+            d3 = TuringDirichlet(d2)
+            @test d1.alpha == d2.alpha == d3.alpha
+            @test d1.alpha0 == d2.alpha0 == d3.alpha0
+            @test d1.lmnB == d2.lmnB == d3.lmnB
+
+            s1 = rand(d1)
+            @test s1 isa Vector{Float64}
+            @test length(s1) == dim
+
+            s2 = rand(d1, n)
+            @test s2 isa Matrix{Float64}
+            @test size(s2) == (dim, n)
+        end
+    end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 90e91560..779e5ec1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,7 +10,7 @@ using Random, LinearAlgebra, Test
 
 using Distributions: meanlogdet
 using DistributionsAD: TuringUniform, TuringMvNormal, TuringMvLogNormal,
-                       TuringPoissonBinomial
+                       TuringPoissonBinomial, TuringDirichlet
 using StatsBase: entropy
 using StatsFuns: binomlogpdf, logsumexp, logistic