diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 5093cf3a5a..522e59165d 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -239,6 +239,7 @@ jobs:
           - ubuntu-latest
         test:
           - DynamicExpressions
+          - Turing
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
@@ -248,8 +249,8 @@ jobs:
       - uses: julia-actions/julia-buildpkg@v1
       - name: "Run tests"
         run: |
-            julia --color=yes --project=test/integration -e 'using Pkg; Pkg.develop([PackageSpec(; path) for path in (".", "lib/EnzymeCore")]); Pkg.instantiate()'
-            julia --color=yes --project=test/integration --threads=auto --check-bounds=yes test/integration/${{ matrix.test }}.jl
+            julia --color=yes --project=test/integration/${{ matrix.test }} -e 'using Pkg; Pkg.develop([PackageSpec(; path) for path in (".", "lib/EnzymeCore")]); Pkg.instantiate()'
+            julia --color=yes --project=test/integration/${{ matrix.test }} --threads=auto --check-bounds=yes test/integration/${{ matrix.test }}/runtests.jl
         shell: bash
   docs:
     name: Documentation
diff --git a/test/integration/Project.toml b/test/integration/DynamicExpressions/Project.toml
similarity index 100%
rename from test/integration/Project.toml
rename to test/integration/DynamicExpressions/Project.toml
diff --git a/test/integration/DynamicExpressions.jl b/test/integration/DynamicExpressions/runtests.jl
similarity index 100%
rename from test/integration/DynamicExpressions.jl
rename to test/integration/DynamicExpressions/runtests.jl
diff --git a/test/integration/Turing/Project.toml b/test/integration/Turing/Project.toml
new file mode 100644
index 0000000000..e9ef3697f4
--- /dev/null
+++ b/test/integration/Turing/Project.toml
@@ -0,0 +1,21 @@
+[deps]
+AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
+AbstractPPL = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
+Bijectors = "76274a88-744f-5084-9051-94815aaf08c4"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+DynamicPPL = "366bfd00-2699-11ea-058f-f148b4cae6d8"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
+FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
+LogDensityProblems = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
+LogDensityProblemsAD = "996a588d-648d-4e1f-a8f0-a84b347e47b1"
+
+[compat]
+AbstractMCMC = "=5.3.0"
+AbstractPPL = "=0.8.4"
+Bijectors = "=0.13.18"
+Distributions = "=0.25.111"
+DynamicPPL = "=0.28.4"
+FiniteDifferences = "0.12.32"
+LogDensityProblems = "=2.1.1"
+LogDensityProblemsAD = "=1.10.0"
diff --git a/test/integration/Turing/runtests.jl b/test/integration/Turing/runtests.jl
new file mode 100644
index 0000000000..7435968961
--- /dev/null
+++ b/test/integration/Turing/runtests.jl
@@ -0,0 +1,99 @@
+module TuringIntegrationTests
+
+using Distributions: Distributions
+using DynamicPPL: DynamicPPL
+using Enzyme: Enzyme
+using FiniteDifferences: FiniteDifferences
+using LinearAlgebra: LinearAlgebra
+using Random: randn
+using Test: @test, @testset
+
+# TODO(mhauru) Could we at some point make do without this?
+Enzyme.API.runtimeActivity!(true)
+
+"""
+Turn a Turing model, possibly with given example values, into a log density function and a
+random value that it can be evaluated at.
+"""
+function build_turing_problem(model)
+    ctx = DynamicPPL.DefaultContext()
+    vi = DynamicPPL.VarInfo(model)
+    vi_linked = DynamicPPL.link(vi, model)
+    ldp = DynamicPPL.LogDensityFunction(vi_linked, model, ctx)
+    test_function = Base.Fix1(DynamicPPL.LogDensityProblems.logdensity, ldp)
+    d = DynamicPPL.LogDensityProblems.dimension(ldp)
+    return test_function, randn(d)
+end
+
+"""
+Test Enzyme.gradient, both Forward and Reverse mode, against FiniteDifferences.grad, for a
+given function f and argument x.
+"""
+function test_grad(f, x; rtol=1e-6, atol=1e-6)
+    finitediff = FiniteDifferences.grad(FiniteDifferences.central_fdm(5, 1), f, x)[1]
+    # TODO(mhauru) The Val(1) works around https://github.com/EnzymeAD/Enzyme.jl/issues/1807
+    @test(
+        collect(Enzyme.gradient(Enzyme.Forward, Enzyme.Const(f), x, Val(1))) ≈ finitediff,
+        rtol = rtol,
+        atol = atol
+    )
+    @test(
+        Enzyme.gradient(Enzyme.Reverse, Enzyme.Const(f), x) ≈ finitediff,
+        rtol = rtol, atol = atol
+    )
+    return nothing
+end
+
+# Turing models to test with. These come from Turing's test suite.
+models = collect(DynamicPPL.TestUtils.DEMO_MODELS)
+
+# Add some other models that use features that have previously been problematic for Enzyme.
+
+DynamicPPL.@model function MvDirichletWithManualAccumulation(w, doc)
+    β ~ DynamicPPL.filldist(Distributions.Dirichlet([1.0, 1.0]), 2)
+    log_product = log.(β)
+    DynamicPPL.@addlogprob! sum(log_product[CartesianIndex.(w, doc)])
+end
+
+push!(models, MvDirichletWithManualAccumulation([1, 1, 1, 1], [1, 1, 2, 2]))
+
+DynamicPPL.@model function demo_lkjchol(d::Int=2)
+    x ~ DynamicPPL.LKJCholesky(d, 1.0)
+    return (x=x,)
+end
+
+push!(models, demo_lkjchol())
+
+DynamicPPL.@model function hmcmatrixsup()
+    return v ~ Distributions.Wishart(7, [1 0.5; 0.5 1])
+end
+
+push!(models, hmcmatrixsup())
+
+DynamicPPL.@model function mvnormal_with_transpose(x=transpose([1.5 2.0;]))
+    m ~ Distributions.MvNormal(LinearAlgebra.Diagonal([1.0, 1.0]))
+    x .~ Distributions.MvNormal(m, LinearAlgebra.Diagonal([1.0, 1.0]))
+    return nothing
+end
+
+push!(models, mvnormal_with_transpose())
+
+DynamicPPL.@model function mvnorm_with_argtype(::Type{TV}=Matrix{Float64}) where {TV}
+    P0 = vcat([0.1 0.0], [0.0 0.1])
+    x = TV(undef, 2, 2)
+    fill!(x, zero(eltype(x)))
+    x[:, 2] ~ Distributions.MvNormal(x[:, 1], P0)
+    return nothing
+end
+
+push!(models, mvnorm_with_argtype())
+
+# Test each model in turn, checking Enzyme's gradient against FiniteDifferences.
+@testset "Turing integration tests" begin
+    @testset "$(typeof(model.f))" for model in models
+        f, x = build_turing_problem(model)
+        test_grad(f, x)
+    end
+end
+
+end