diff --git a/src/bijectors/product_bijector.jl b/src/bijectors/product_bijector.jl
new file mode 100644
index 00000000..94cd1fb1
--- /dev/null
+++ b/src/bijectors/product_bijector.jl
@@ -0,0 +1,66 @@
+struct ProductBijector{Bs,N} <: Transform
+    bs::Bs
+end
+
+ProductBijector(bs::AbstractArray{<:Any,N}) where {N} = ProductBijector{typeof(bs),N}(bs)
+
+inverse(b::ProductBijector) = ProductBijector(map(inverse, b.bs))
+
+function _product_bijector_check_dim(::Val{N}, ::Val{M}) where {N,M}
+    if N > M
+        throw(
+            DimensionMismatch(
+                "Number of bijectors needs to be smaller than or equal to the number of dimensions",
+            ),
+        )
+    end
+end
+
+function _product_bijector_slices(
+    ::ProductBijector{<:AbstractArray,N}, x::AbstractArray{<:Real,M}
+) where {N,M}
+    _product_bijector_check_dim(Val(N), Val(M))
+
+    # If N < M, then the bijectors expect an input vector of dimension `M - N`.
+    # To achieve this, we need to slice along the last `N` dimensions.
+    return eachslice(x; dims=ntuple(i -> i + (M - N), N))
+end
+
+# Specialization for case where we're just applying elementwise.
+function transform(
+    b::ProductBijector{<:AbstractArray,N}, x::AbstractArray{<:Real,N}
+) where {N}
+    return map(transform, b.bs, x)
+end
+# General case.
+function transform(
+    b::ProductBijector{<:AbstractArray,N}, x::AbstractArray{<:Real,M}
+) where {N,M}
+    slices = _product_bijector_slices(b, x)
+    return stack(map(transform, b.bs, slices))
+end
+
+function with_logabsdet_jacobian(
+    b::ProductBijector{<:AbstractArray,N}, x::AbstractArray{<:Real,N}
+) where {N}
+    results = map(with_logabsdet_jacobian, b.bs, x)
+    return map(first, results), sum(last, results)
+end
+function with_logabsdet_jacobian(
+    b::ProductBijector{<:AbstractArray,N}, x::AbstractArray{<:Real,M}
+) where {N,M}
+    slices = _product_bijector_slices(b, x)
+    results = map(with_logabsdet_jacobian, b.bs, slices)
+    return stack(map(first, results)), sum(last, results)
+end
+
+# Other utilities.
+function output_size(b::ProductBijector{<:AbstractArray,N}, sz::NTuple{M}) where {N,M}
+    _product_bijector_check_dim(Val(N), Val(M))
+
+    sz_redundant = ntuple(i -> sz[i + (M - N)], N)
+    sz_example = ntuple(i -> sz[i], M - N)
+    # NOTE: `Base.stack`, which is used in the transformation, only supports the scenario where
+    # all `b.bs` have the same output sizes => only need to check the first one.
+    return (output_size(first(b.bs), sz_example)..., sz_redundant...)
+end
diff --git a/src/interface.jl b/src/interface.jl
index 1ba9aa60..0b84523c 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -251,6 +251,7 @@ include("bijectors/corr.jl")
 include("bijectors/truncated.jl")
 include("bijectors/named_bijector.jl")
 include("bijectors/ordered.jl")
+include("bijectors/product_bijector.jl")
 
 # Normalizing flow related
 include("bijectors/planar_layer.jl")
diff --git a/src/transformed_distribution.jl b/src/transformed_distribution.jl
index 0126db05..65a3e69c 100644
--- a/src/transformed_distribution.jl
+++ b/src/transformed_distribution.jl
@@ -66,6 +66,11 @@ has_constant_bijector(d::Type{<:KSOneSided}) = true
 function has_constant_bijector(::Type{<:Product{Continuous,D}}) where {D}
     return has_constant_bijector(D)
 end
+function has_constant_bijector(
+    ::Type{<:Distributions.ProductDistribution{<:Any,<:Any,A}}
+) where {A}
+    return has_constant_bijector(eltype(A))
+end
 
 # Container distributions.
 bijector(d::DiscreteUnivariateDistribution) = identity
@@ -93,6 +98,22 @@ end
     end
 end
 
+function bijector(d::Distributions.ProductDistribution{N,0,A}) where {N,A}
+    # This is the univariate scenario, so if we have a constant bijector
+    # we can just use the same one for all elements.
+    return if has_constant_bijector(eltype(A))
+        elementwise(bijector(d.dists[1]))
+    else
+        ProductBijector(map(bijector, d.dists))
+    end
+end
+
+function bijector(d::Distributions.ProductDistribution{N,M,A}) where {N,M,A}
+    dists = d.dists
+    bs = bijector.(dists)
+    return ProductBijector{typeof(bs),N - M}(bs)
+end
+
 # Specialized implementations.
 bijector(d::Normal) = identity
 bijector(d::Distributions.AbstractMvNormal) = identity
diff --git a/test/Project.toml b/test/Project.toml
index f20d117b..39875f6e 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -3,6 +3,7 @@ ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 DistributionsAD = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
+FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
@@ -21,6 +22,7 @@ ChainRulesTestUtils = "0.7, 1"
 ChangesOfVariables = "0.1"
 Combinatorics = "1.0.2"
 DistributionsAD = "0.6.3"
+FillArrays = "1"
 FiniteDifferences = "0.11, 0.12"
 ForwardDiff = "0.10.12"
 Functors = "0.1, 0.2, 0.3, 0.4"
diff --git a/test/bijectors/product_bijector.jl b/test/bijectors/product_bijector.jl
new file mode 100644
index 00000000..818f89c0
--- /dev/null
+++ b/test/bijectors/product_bijector.jl
@@ -0,0 +1,69 @@
+using Bijectors: ProductBijector
+using FillArrays
+
+has_square_jacobian(b, x) = Bijectors.output_size(b, x) == size(x)
+
+@testset "ProductBijector" begin
+    # Some distributions.
+    ds = [
+        # 1D.
+        (Normal(), true),
+        (InverseGamma(), false),
+        (Beta(), false),
+        # 2D.
+        (MvNormal(Zeros(3), I), true),
+        (Dirichlet(Ones(3)), false),
+    ]
+
+    # Stacking a single dimension.
+    N = 4
+    @testset "Single-dim stack: $(nameof(typeof(d)))" for (d, isidentity) in ds
+        b = bijector(d)
+        xs = [rand(d) for _ in 1:N]
+        x = stack(xs)
+
+        d_prod = product_distribution(Fill(d, N))
+        b_prod = bijector(d_prod)
+
+        sz_true = (Bijectors.output_size(b, size(xs[1]))..., N)
+        @test Bijectors.output_size(b_prod, size(x)) == sz_true
+
+        results = map(xs) do x
+            with_logabsdet_jacobian(b, x)
+        end
+        y, logjac = stack(map(first, results)), sum(last, results)
+
+        test_bijector(
+            b_prod,
+            x;
+            y,
+            logjac,
+            changes_of_variables_test=has_square_jacobian(b, xs[1]),
+            test_not_identity=!isidentity,
+        )
+    end
+
+    @testset "Two-dim stack: $(nameof(typeof(d)))" for (d, isidentity) in ds
+        b = bijector(d)
+        xs = [rand(d) for _ in 1:N, _ in 1:(N + 1)]
+        x = stack(xs)
+
+        d_prod = product_distribution(Fill(d, N, N + 1))
+        b_prod = bijector(d_prod)
+
+        sz_true = (Bijectors.output_size(b, size(xs[1]))..., N, N + 1)
+        @test Bijectors.output_size(b_prod, size(x)) == sz_true
+
+        results = map(Base.Fix1(with_logabsdet_jacobian, b), xs)
+        y, logjac = stack(map(first, results)), sum(last, results)
+
+        test_bijector(
+            b_prod,
+            x;
+            y,
+            logjac,
+            changes_of_variables_test=has_square_jacobian(b, xs[1]),
+            test_not_identity=!isidentity,
+        )
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 5c4f2df6..01b81fb8 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -48,6 +48,7 @@ if GROUP == "All" || GROUP == "Interface"
     include("bijectors/pd.jl")
     include("bijectors/reshape.jl")
     include("bijectors/corr.jl")
+    include("bijectors/product_bijector.jl")
 
     include("distributionsad.jl")
 end