diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 87cc04fc8..aed689adb 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -31,6 +31,7 @@ jobs:
           - 'ext/nnlib'
           - 'ext/special_functions'
           - 'integration_testing/array'
+          - 'integration_testing/bijectors'
           - 'integration_testing/diff_tests'
           - 'integration_testing/distributions'
           - 'integration_testing/gp'
diff --git a/test/integration_testing/bijectors/Project.toml b/test/integration_testing/bijectors/Project.toml
new file mode 100644
index 000000000..54a732057
--- /dev/null
+++ b/test/integration_testing/bijectors/Project.toml
@@ -0,0 +1,5 @@
+[deps]
+Bijectors = "76274a88-744f-5084-9051-94815aaf08c4"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
diff --git a/test/integration_testing/bijectors/bijectors.jl b/test/integration_testing/bijectors/bijectors.jl
new file mode 100644
index 000000000..9a2a7fa4b
--- /dev/null
+++ b/test/integration_testing/bijectors/bijectors.jl
@@ -0,0 +1,134 @@
+using Pkg
+Pkg.activate(@__DIR__)
+Pkg.develop(; path = joinpath(@__DIR__, "..", "..", ".."))
+
+using Bijectors: Bijectors
+using LinearAlgebra: LinearAlgebra
+using Random: randn
+
+"""
+Type for specifying a test case for `test_rule`.
+"""
+struct TestCase
+    func::Function
+    arg::Any
+    name::Union{String,Nothing}
+    broken::Bool
+end
+
+TestCase(f, arg; name = nothing, broken=false) = TestCase(f, arg, name, broken)
+
+"""
+A helper function that returns a TestCase that evaluates bijector(inverse(bijector)(x))
+"""
+function b_binv_test_case(bijector, dim; name = nothing, rng = Xoshiro(23))
+    if name === nothing
+        name = string(bijector)
+    end
+    b_inv = Bijectors.inverse(bijector)
+    return TestCase(x -> bijector(b_inv(x)), randn(rng, dim); name = name)
+end
+
+@testset "Bijectors integration tests" begin
+    test_cases = TestCase[
+        b_binv_test_case(Bijectors.VecCorrBijector(), 3),
+        b_binv_test_case(Bijectors.VecCorrBijector(), 0),
+        b_binv_test_case(Bijectors.CorrBijector(), (3, 3)),
+        b_binv_test_case(Bijectors.CorrBijector(), (0, 0)),
+        b_binv_test_case(Bijectors.VecCholeskyBijector(:L), 3),
+        b_binv_test_case(Bijectors.VecCholeskyBijector(:L), 0),
+        b_binv_test_case(Bijectors.VecCholeskyBijector(:U), 3),
+        b_binv_test_case(Bijectors.VecCholeskyBijector(:U), 0),
+        b_binv_test_case(
+            Bijectors.Coupling(Bijectors.Shift, Bijectors.PartitionMask(3, [1], [2])),
+            3,
+        ),
+        b_binv_test_case(Bijectors.InvertibleBatchNorm(3), (3, 3)),
+        b_binv_test_case(Bijectors.LeakyReLU(0.2), 3),
+        b_binv_test_case(Bijectors.Logit(0.1, 0.3), 3),
+        b_binv_test_case(Bijectors.PDBijector(), (3, 3)),
+        b_binv_test_case(Bijectors.PDVecBijector(), 3),
+        b_binv_test_case(Bijectors.Permute([
+            0 1 0
+            1 0 0
+            0 0 1
+        ]), (3, 3)),
+        b_binv_test_case(Bijectors.PlanarLayer(3), (3, 3)),
+        b_binv_test_case(Bijectors.RadialLayer(3), 3),
+        b_binv_test_case(Bijectors.Reshape((2, 3), (3, 2)), (2, 3)),
+        b_binv_test_case(Bijectors.Scale(0.2), 3),
+        b_binv_test_case(Bijectors.Shift(-0.4), 3),
+        b_binv_test_case(Bijectors.SignFlip(), 3),
+        b_binv_test_case(Bijectors.SimplexBijector(), 3),
+        b_binv_test_case(Bijectors.TruncatedBijector(-0.2, 0.5), 3),
+
+        # Below, some test cases that don't fit the b_binv_test_case mold.
+
+        TestCase(
+            function (x)
+                b = Bijectors.RationalQuadraticSpline(
+                    [-0.2, 0.1, 0.5],
+                    [-0.3, 0.3, 0.9],
+                    [1.0, 0.2, 1.0],
+                )
+                binv = Bijectors.inverse(b)
+                return binv(b(x))
+            end,
+            randn(Xoshiro(23));
+            name = "RationalQuadraticSpline on scalar",
+        ),
+        TestCase(
+            function (x)
+                b = Bijectors.OrderedBijector()
+                binv = Bijectors.inverse(b)
+                return binv(b(x))
+            end,
+            randn(Xoshiro(23), 7);
+            name = "OrderedBijector",
+        ),
+        TestCase(
+            function (x)
+                layer = Bijectors.PlanarLayer(x[1:2], x[3:4], x[5:5])
+                flow = Bijectors.transformed(
+                    Bijectors.MvNormal(zeros(2), LinearAlgebra.I),
+                    layer,
+                )
+                x = x[6:7]
+                return Bijectors.logpdf(flow.dist, x) -
+                       Bijectors.logabsdetjac(flow.transform, x)
+            end,
+            randn(Xoshiro(23), 7);
+            name = "PlanarLayer7",
+            # TODO(mhauru) Broken on v1.11 due to
+            # https://github.com/compintell/Mooncake.jl/issues/319
+            broken=(VERSION >= v"1.11"),
+        ),
+        TestCase(
+            function (x)
+                layer = Bijectors.PlanarLayer(x[1:2], x[3:4], x[5:5])
+                flow = Bijectors.transformed(
+                    Bijectors.MvNormal(zeros(2), LinearAlgebra.I),
+                    layer,
+                )
+                x = reshape(x[6:end], 2, :)
+                return sum(
+                    Bijectors.logpdf(flow.dist, x) -
+                    Bijectors.logabsdetjac(flow.transform, x),
+                )
+            end,
+            randn(Xoshiro(23), 11);
+            name = "PlanarLayer11",
+        ),
+    ]
+
+    @testset "$(case.name)" for case in test_cases
+        if case.broken
+            @test_broken begin
+                test_rule(Xoshiro(123456), case.func, case.arg; is_primitive=false)
+                true
+            end
+        else
+            test_rule(Xoshiro(123456), case.func, case.arg; is_primitive=false)
+        end
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index e28bbd470..dd9d955ea 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -69,6 +69,8 @@ include("front_matter.jl")
         include(joinpath("ext", "special_functions", "special_functions.jl"))
     elseif test_group == "integration_testing/array"
         include(joinpath("integration_testing", "array.jl"))
+    elseif test_group == "integration_testing/bijectors"
+        include(joinpath("integration_testing", "bijectors", "bijectors.jl"))
     elseif test_group == "integration_testing/diff_tests"
         include(joinpath("integration_testing", "diff_tests.jl"))
     elseif test_group == "integration_testing/distributions"