diff --git a/Project.toml b/Project.toml
index d85df8388..b172bcaee 100644
--- a/Project.toml
+++ b/Project.toml
@@ -29,7 +29,7 @@ ADTypes = "0.2"
 AbstractMCMC = "5"
 AbstractPPL = "0.7"
 BangBang = "0.3"
-Bijectors = "0.13"
+Bijectors = "0.13.9"
 ChainRulesCore = "1"
 Compat = "4"
 ConstructionBase = "1.5.4"
diff --git a/src/abstract_varinfo.jl b/src/abstract_varinfo.jl
index bd7e8d8fb..a12de6154 100644
--- a/src/abstract_varinfo.jl
+++ b/src/abstract_varinfo.jl
@@ -765,6 +765,16 @@ function with_logabsdet_jacobian_and_reconstruct(f, dist, x)
     return with_logabsdet_jacobian(f, x_recon)
 end
 
+# NOTE: Necessary to handle product distributions of `Dirichlet` and similar.
+function with_logabsdet_jacobian_and_reconstruct(
+    f::Bijectors.Inverse{<:Bijectors.SimplexBijector}, dist, y
+)
+    (d, ns...) = size(dist)
+    yreshaped = reshape(y, d - 1, ns...)
+    x, logjac = with_logabsdet_jacobian(f, yreshaped)
+    return x, logjac
+end
+
 # TODO: Once `(inv)link` isn't used heavily in `getindex(vi, vn)`, we can
 # just use `first ∘ with_logabsdet_jacobian` to reduce the maintenance burden.
 # NOTE: `reconstruct` is no-op if `val` is already of correct shape.
diff --git a/src/utils.jl b/src/utils.jl
index b447fed53..1457677be 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -237,6 +237,11 @@ reconstruct(f, dist, val) = reconstruct(dist, val)
 reconstruct(::UnivariateDistribution, val::Real) = val
 reconstruct(::MultivariateDistribution, val::AbstractVector{<:Real}) = copy(val)
 reconstruct(::MatrixDistribution, val::AbstractMatrix{<:Real}) = copy(val)
+function reconstruct(
+    ::Distribution{ArrayLikeVariate{N}}, val::AbstractArray{<:Real,N}
+) where {N}
+    return copy(val)
+end
 reconstruct(::Inverse{Bijectors.VecCorrBijector}, ::LKJ, val::AbstractVector) = copy(val)
 
 function reconstruct(dist::LKJCholesky, val::AbstractVector{<:Real})
diff --git a/test/linking.jl b/test/linking.jl
index 9103fff67..06f6fb6d6 100644
--- a/test/linking.jl
+++ b/test/linking.jl
@@ -174,4 +174,29 @@ end
             end
         end
     end
+
+    # Related: https://github.com/TuringLang/Turing.jl/issues/2190
+    @testset "High-dim Dirichlet" begin
+        @model function demo_highdim_dirichlet(ns...)
+            return x ~ filldist(Dirichlet(ones(2)), ns...)
+        end
+        @testset "ns=$ns" for ns in [
+            (3,),
+            # TODO: Uncomment once we have https://github.com/TuringLang/Bijectors.jl/pull/304
+            # (3, 4), (3, 4, 5)
+        ]
+            model = demo_highdim_dirichlet(ns...)
+            example_values = rand(NamedTuple, model)
+            vis = DynamicPPL.TestUtils.setup_varinfos(model, example_values, (@varname(x),))
+            @testset "$(short_varinfo_name(vi))" for vi in vis
+                # Linked.
+                vi_linked = if mutable
+                    DynamicPPL.link!!(deepcopy(vi), model)
+                else
+                    DynamicPPL.link(vi, model)
+                end
+                @test length(vi_linked[:]) == prod(ns)
+            end
+        end
+    end
 end