diff --git a/Project.toml b/Project.toml
index b5357221..36e54d04 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "DistributionsAD"
 uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
-version = "0.6.16"
+version = "0.6.17"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/multivariate.jl b/src/multivariate.jl
index c41734f1..0f388ebb 100644
--- a/src/multivariate.jl
+++ b/src/multivariate.jl
@@ -63,14 +63,9 @@ ZygoteRules.@adjoint function Distributions.Dirichlet(d, alpha)
     return ZygoteRules.pullback(TuringDirichlet, d, alpha)
 end
 
-function simplex_logpdf(alpha, lmnB, x::AbstractVector)
-    sum((alpha .- 1) .* log.(x)) - lmnB
-end
+simplex_logpdf(alpha, lmnB, x::AbstractVector) = sum(xlogy.(alpha .- 1, x)) - lmnB
 function simplex_logpdf(alpha, lmnB, x::AbstractMatrix)
-    @views init = vcat(sum((alpha .- 1) .* log.(x[:,1])) - lmnB)
-    mapreduce(vcat, drop(eachcol(x), 1); init = init) do c
-        sum((alpha .- 1) .* log.(c)) - lmnB
-    end
+    return vec(sum(xlogy.(alpha .- 1, x); dims=1)) .- lmnB
 end
 
 ZygoteRules.@adjoint function simplex_logpdf(alpha, lmnB, x::AbstractVector)
diff --git a/src/reversediff.jl b/src/reversediff.jl
index 6ced110b..a4c9f42b 100644
--- a/src/reversediff.jl
+++ b/src/reversediff.jl
@@ -18,7 +18,8 @@ using ..DistributionsAD: DistributionsAD
 
 
 import SpecialFunctions, NaNMath
-import ..DistributionsAD: turing_chol, symm_turing_chol, _mv_categorical_logpdf, adapt_randn
+import ..DistributionsAD: turing_chol, symm_turing_chol, _mv_categorical_logpdf, adapt_randn,
+    simplex_logpdf
 import Base.Broadcast: materialize
 import StatsFuns: logsumexp
 
@@ -47,12 +48,25 @@ using ..DistributionsAD: TuringPoissonBinomial,
                          TuringDirichlet,
                          TuringScalMvNormal,
                          TuringDiagMvNormal,
-                         TuringDenseMvNormal
+                         TuringDenseMvNormal,
+                         VectorOfMultivariate,
+                         FillVectorOfMultivariate
 
 include("reversediffx.jl")
 
 adapt_randn(rng::Random.AbstractRNG, x::TrackedArray, dims...) = adapt_randn(rng, value(x), dims...)
 
+# without this definition tests of `VectorOfMultivariate` with `Dirichlet` fail
+# upstream bug caused by `view` + `track`: https://github.com/JuliaDiff/ReverseDiff.jl/pull/164
+function _logpdf(dist::VectorOfMultivariate, x::AbstractMatrix{<:TrackedReal})
+    return sum(i -> _logpdf(dist.dists[i], x[:, i]), axes(x, 2))
+end
+
+# fix method ambiguity
+function _logpdf(dist::FillVectorOfMultivariate, x::AbstractMatrix{<:TrackedReal})
+    return loglikelihood(dist.dists.value, x)
+end
+
 function PoissonBinomial(p::TrackedArray{<:Real}; check_args=true)
     return TuringPoissonBinomial(p; check_args = check_args)
 end
@@ -240,36 +254,60 @@ end
 # zero mean,, constant variance
 MvLogNormal(d::Int, σ::TrackedReal) = TuringMvLogNormal(TuringMvNormal(d, σ))
 
-Dirichlet(alpha::TrackedVector) = TuringDirichlet(alpha)
+# Dirichlet
+
+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)
+end
+function logpdf(d::Dirichlet, x::AbstractMatrix{<:TrackedReal})
+    return logpdf(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+end
+function loglikelihood(d::Dirichlet, x::AbstractMatrix{<:TrackedReal})
+    return loglikelihood(TuringDirichlet(d.alpha, d.alpha0, d.lmnB), x)
+end
+
+# default definition of `loglikelihood` yields gradients of zero?!
+# upstream bug caused by `view` + `track`: https://github.com/JuliaDiff/ReverseDiff.jl/pull/164
+function loglikelihood(d::TuringDirichlet, x::AbstractMatrix{<:TrackedReal})
+    return sum(i -> logpdf(d, x[:, i]), axes(x, 2))
+end
+
 for func_header in [
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::Real, x::AbstractVector)),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::Real, x::AbstractVector)),
     :(simplex_logpdf(alpha::AbstractVector, lmnB::TrackedReal, x::AbstractVector)),
-    :(simplex_logpdf(alpha::AbstractVector, lmnB::Real, x::TrackedVector)),
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::TrackedReal, x::AbstractVector)),
-    :(simplex_logpdf(alpha::AbstractVector, lmnB::TrackedReal, x::TrackedVector)),
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::Real, x::TrackedVector)),
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::TrackedReal, x::TrackedVector)),
+    :(simplex_logpdf(alpha::AbstractVector, lmnB::Real, x::AbstractVector{<:TrackedReal})),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::TrackedReal, x::AbstractVector)),
+    :(simplex_logpdf(alpha::AbstractVector, lmnB::TrackedReal, x::AbstractVector{<:TrackedReal})),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::Real, x::AbstractVector{<:TrackedReal})),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::TrackedReal, x::AbstractVector{<:TrackedReal})),
 
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::Real, x::AbstractMatrix)),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::Real, x::AbstractMatrix)),
     :(simplex_logpdf(alpha::AbstractVector, lmnB::TrackedReal, x::AbstractMatrix)),
-    :(simplex_logpdf(alpha::AbstractVector, lmnB::Real, x::TrackedMatrix)),
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::TrackedReal, x::AbstractMatrix)),
-    :(simplex_logpdf(alpha::AbstractVector, lmnB::TrackedReal, x::TrackedMatrix)),
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::Real, x::TrackedMatrix)),
-    :(simplex_logpdf(alpha::TrackedVector, lmnB::TrackedReal, x::TrackedMatrix)),
+    :(simplex_logpdf(alpha::AbstractVector, lmnB::Real, x::AbstractMatrix{<:TrackedReal})),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::TrackedReal, x::AbstractMatrix)),
+    :(simplex_logpdf(alpha::AbstractVector, lmnB::TrackedReal, x::AbstractMatrix{<:TrackedReal})),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::Real, x::AbstractMatrix{<:TrackedReal})),
+    :(simplex_logpdf(alpha::AbstractVector{<:TrackedReal}, lmnB::TrackedReal, x::AbstractMatrix{<:TrackedReal})),
 ]
     @eval $func_header = track(simplex_logpdf, alpha, lmnB, x)
 end
 @grad function simplex_logpdf(alpha, lmnB, x::AbstractVector)
-    simplex_logpdf(value(alpha), value(lmnB), value(x)), Δ -> begin
-        (Δ .* log.(value(x)), -Δ, Δ .* (value(alpha) .- 1))
+    _alpha = value(alpha)
+    _lmnB = value(lmnB)
+    _x = value(x)
+    simplex_logpdf(_alpha, _lmnB, _x), Δ -> begin
+        (Δ .* log.(_x), -Δ, Δ .* (_alpha .- 1) ./ _x)
     end
 end
 @grad function simplex_logpdf(alpha, lmnB, x::AbstractMatrix)
-    simplex_logpdf(value(alpha), value(lmnB), value(x)), Δ -> begin
-        (log.(value(x)) * Δ, -sum(Δ), repeat(value(alpha) .- 1, 1, size(x, 2)) * Diagonal(Δ))
+    _alpha = value(alpha)
+    _lmnB = value(lmnB)
+    _x = value(x)
+    simplex_logpdf(_alpha, _lmnB, _x), Δ -> begin
+        (log.(_x) * Δ, -sum(Δ), ((_alpha .- 1) ./ _x) * Diagonal(Δ))
     end
 end
 
diff --git a/test/Project.toml b/test/Project.toml
index 5271e9cf..d1bbbba4 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -21,7 +21,7 @@ Combinatorics = "1.0.2"
 Distributions = "0.24.3"
 FiniteDifferences = "0.11.3, 0.12"
 ForwardDiff = "0.10.12"
-NNlib = "0.7.7"
+NNlib = "0.7.10"
 PDMats = "0.10.1"
 ReverseDiff = "1.4.4"
 StatsBase = "0.33.2"
diff --git a/test/ad/distributions.jl b/test/ad/distributions.jl
index a543a5dd..90b541c6 100644
--- a/test/ad/distributions.jl
+++ b/test/ad/distributions.jl
@@ -26,10 +26,6 @@
     to_positive(x) = exp.(x)
     to_positive(x::AbstractArray{<:AbstractArray}) = to_positive.(x)
 
-    # Create vectors in probability simplex.
-    to_simplex(x::AbstractArray; dims=1) = NNlib.softmax(x; dims=dims)
-    to_simplex(x::AbstractArray{<:AbstractArray}; dims=1) = to_simplex.(x; dims=dims)
-
     # Tests that have a `broken` field can be executed but, according to FiniteDifferences,
     # fail to produce the correct result. These tests can be checked with `@test_broken`.
     univariate_distributions = DistSpec[
diff --git a/test/runtests.jl b/test/runtests.jl
index 9f2d7773..90e91560 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -45,11 +45,32 @@ if GROUP == "All" || GROUP == "AD"
     to_posdef(A::AbstractMatrix) = A * A' + I
     to_posdef_diagonal(a::AbstractVector) = Diagonal(a.^2 .+ 1)
 
+    # Create vectors in probability simplex.
+    to_simplex(x::AbstractArray) = NNlib.softmax(x; dims=1)
+    to_simplex(x::AbstractArray{<:AbstractArray}) = to_simplex.(x)
+
+    if AD == "All" || AD == "ReverseDiff"
+        @eval begin
+            # Define adjoint for ReverseDiff
+            function to_simplex(x::AbstractArray{<:ReverseDiff.TrackedReal})
+                return ReverseDiff.track(to_simplex, x)
+            end
+            ReverseDiff.@grad function to_simplex(x)
+                _x = ReverseDiff.value(x)
+                y = to_simplex(_x)
+                function pullback(∇)
+                    return (NNlib.∇softmax(∇, _x, y; dims=1),)
+                end
+                return y, pullback
+            end
+        end
+    end
+
     if AD == "All" || AD == "Tracker"
         @eval begin
             # Define adjoints for Tracker
-            to_posdef(A::TrackedMatrix) = Tracker.track(to_posdef, A)
-            Tracker.@grad function to_posdef(A::TrackedMatrix)
+            to_posdef(A::Tracker.TrackedMatrix) = Tracker.track(to_posdef, A)
+            Tracker.@grad function to_posdef(A::Tracker.TrackedMatrix)
                 data_A = Tracker.data(A)
                 S = data_A * data_A' + I
                 function pullback(∇)