diff --git a/src/compat/distributionsad.jl b/src/compat/distributionsad.jl
index 080097f3..99dc81d5 100644
--- a/src/compat/distributionsad.jl
+++ b/src/compat/distributionsad.jl
@@ -13,8 +13,8 @@ bijector(::TuringScalMvNormal) = identity
 bijector(::TuringDiagMvNormal) = identity
 bijector(::TuringDenseMvNormal) = identity
 
-bijector(d::FillVectorOfUnivariate{Continuous}) = bijector(d.v.value)
-bijector(d::FillMatrixOfUnivariate{Continuous}) = up1(bijector(d.dists.value))
+bijector(d::FillVectorOfUnivariate{Continuous}) = elementwise(bijector(d.v.value))
+bijector(d::FillMatrixOfUnivariate{Continuous}) = elementwise(bijector(d.dists.value))
 bijector(d::MatrixOfUnivariate{Discrete}) = identity
 bijector(d::MatrixOfUnivariate{Continuous}) = TruncatedBijector(_minmax(d.dists)...)
 bijector(d::VectorOfMultivariate{Discrete}) = identity
@@ -30,7 +30,7 @@ for T in (:VectorOfMultivariate, :FillVectorOfMultivariate)
         bijector(d::$T{Continuous, <:TuringDirichlet}) = SimplexBijector()
     end
 end
-bijector(d::FillVectorOfMultivariate{Continuous}) = bijector(d.dists.value)
+bijector(d::FillVectorOfMultivariate{Continuous}) = columnwise(bijector(d.dists.value))
 
 isdirichlet(::VectorOfMultivariate{Continuous, <:Dirichlet}) = true
 isdirichlet(::VectorOfMultivariate{Continuous, <:TuringDirichlet}) = true
diff --git a/src/interface.jl b/src/interface.jl
index a216a921..14724943 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -17,6 +17,20 @@ elementwise(f) = Base.Fix1(broadcast, f)
 # TODO: This is makes dispatching quite a bit easier, but uncertain if this is really
 # the way to go.
 elementwise(f::ComposedFunction) = ComposedFunction(elementwise(f.outer), elementwise(f.inner))
+const Columnwise{F} = Base.Fix1{typeof(eachcolmaphcat),F}
+"""
+
+Alias for `Base.Fix1(eachcolmaphcat, f)`.
+
+Represents a function `f` which is applied to each column of an input.
+"""
+columnwise(f) = Base.Fix1(eachcolmaphcat, f)
+
+transform(f::Columnwise, x::AbstractMatrix) = f(x)
+function logabsdetjac(f::Columnwise, x::AbstractMatrix)
+    return sum(Base.Fix1(logabsdetjac, f.x), eachcol(x))
+end
+with_logabsdet_jacobian(f::Columnwise, x::AbstractMatrix) = (f(x), logabsdetjac(f, x))
 
 ######################
 # Bijector interface #