diff --git a/DifferentiationInterface/docs/src/explanation/backends.md b/DifferentiationInterface/docs/src/explanation/backends.md
index 013d9e7c8..cb43633ee 100644
--- a/DifferentiationInterface/docs/src/explanation/backends.md
+++ b/DifferentiationInterface/docs/src/explanation/backends.md
@@ -95,7 +95,7 @@ In general, using a forward outer backend over a reverse inner backend will yiel
 The wrapper [`DifferentiateWith`](@ref) allows you to switch between backends.
 It takes a function `f` and specifies that `f` should be differentiated with the substitute backend of your choice, instead of whatever true backend the surrounding code is trying to use.
 In other words, when someone tries to differentiate `dw = DifferentiateWith(f, substitute_backend)` with `true_backend`, then `substitute_backend` steps in and `true_backend` does not dive into the function `f` itself.
-At the moment, `DifferentiateWith` only works when `true_backend` is either [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) or a [ChainRules.jl](https://github.com/JuliaDiff/ChainRules.jl)-compatible backend.
+At the moment, `DifferentiateWith` only works when `true_backend` is either [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl), [Mooncake.jl](https://github.com/chalk-lab/Mooncake.jl), or a [ChainRules.jl](https://github.com/JuliaDiff/ChainRules.jl)-compatible backend (e.g., [Zygote.jl](https://github.com/FluxML/Zygote.jl)).
 
 ## Implementations
 
diff --git a/DifferentiationInterface/docs/src/faq/differentiability.md b/DifferentiationInterface/docs/src/faq/differentiability.md
index 197384c4f..5845e80f5 100644
--- a/DifferentiationInterface/docs/src/faq/differentiability.md
+++ b/DifferentiationInterface/docs/src/faq/differentiability.md
@@ -111,4 +111,5 @@ There are, however, translation utilities:
 ### Backend switch
 
 Also note the existence of [`DifferentiationInterface.DifferentiateWith`](@ref), which allows the user to wrap a function that should be differentiated with a specific backend.
-Right now it only targets ForwardDiff.jl and ChainRulesCore.jl, but PRs are welcome to define Enzyme.jl and Mooncake.jl rules for this object.
\ No newline at end of file
+
+Right now, it only targets [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl), [Mooncake.jl](), [ChainRules.jl](https://juliadiff.org/ChainRulesCore.jl/stable/)-compatible backends (e.g., [Zygote.jl](https://github.com/FluxML/Zygote.jl)), but PRs are welcome to define Enzyme.jl rules for this object.
\ No newline at end of file
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceChainRulesCoreExt/differentiate_with.jl b/DifferentiationInterface/ext/DifferentiationInterfaceChainRulesCoreExt/differentiate_with.jl
index 23f9c9b0c..292372b81 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceChainRulesCoreExt/differentiate_with.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceChainRulesCoreExt/differentiate_with.jl
@@ -1,7 +1,7 @@
 function ChainRulesCore.rrule(dw::DI.DifferentiateWith, x)
     (; f, backend) = dw
     y = f(x)
-    prep_same = DI.prepare_pullback_same_point_nokwarg(Val(true), f, backend, x, (y,))
+    prep_same = DI.prepare_pullback_same_point_nokwarg(Val(false), f, backend, x, (y,))
     function pullbackfunc(dy)
         tx = DI.pullback(f, prep_same, backend, x, (dy,))
         return (NoTangent(), only(tx))
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl
index 6253ea229..321378e23 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/DifferentiationInterfaceMooncakeExt.jl
@@ -3,6 +3,7 @@ module DifferentiationInterfaceMooncakeExt
 using ADTypes: ADTypes, AutoMooncake
 import DifferentiationInterface as DI
 using Mooncake:
+    Mooncake,
     CoDual,
     Config,
     prepare_gradient_cache,
@@ -11,6 +12,16 @@ using Mooncake:
     value_and_gradient!!,
     value_and_pullback!!,
     zero_tangent,
+    rdata_type,
+    fdata,
+    rdata,
+    tangent_type,
+    NoTangent,
+    @is_primitive,
+    zero_fcodual,
+    MinimalCtx,
+    NoRData,
+    primal,
     _copy_output,
     _copy_to_output!!
 
@@ -25,5 +36,6 @@ mycopy(x) = deepcopy(x)
 
 include("onearg.jl")
 include("twoarg.jl")
+include("differentiate_with.jl")
 
 end
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/differentiate_with.jl b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/differentiate_with.jl
new file mode 100644
index 000000000..3b4fb91c3
--- /dev/null
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/differentiate_with.jl
@@ -0,0 +1,84 @@
+@is_primitive MinimalCtx Tuple{DI.DifferentiateWith,<:Any}
+
+struct MooncakeDifferentiateWithError <: Exception
+    F::Type
+    X::Type
+    Y::Type
+    function MooncakeDifferentiateWithError(::F, ::X, ::Y) where {F,X,Y}
+        return new(F, X, Y)
+    end
+end
+
+function Base.showerror(io::IO, e::MooncakeDifferentiateWithError)
+    return print(
+        io,
+        "MooncakeDifferentiateWithError: For the function type $(e.F) and input type $(e.X), the output type $(e.Y) is currently not supported.",
+    )
+end
+
+function Mooncake.rrule!!(dw::CoDual{<:DI.DifferentiateWith}, x::CoDual{<:Number})
+    primal_func = primal(dw)
+    primal_x = primal(x)
+    (; f, backend) = primal_func
+    y = zero_fcodual(f(primal_x))
+
+    # output is a vector, so we need to use the vector pullback
+    function pullback_array!!(dy::NoRData)
+        tx = DI.pullback(f, backend, primal_x, (y.dx,))
+        @assert rdata(only(tx)) isa rdata_type(tangent_type(typeof(primal_x)))
+        return NoRData(), rdata(only(tx))
+    end
+
+    # output is a scalar, so we can use the scalar pullback
+    function pullback_scalar!!(dy::Number)
+        tx = DI.pullback(f, backend, primal_x, (dy,))
+        @assert rdata(only(tx)) isa rdata_type(tangent_type(typeof(primal_x)))
+        return NoRData(), rdata(only(tx))
+    end
+
+    pullback = if primal(y) isa Number
+        pullback_scalar!!
+    elseif primal(y) isa AbstractArray
+        pullback_array!!
+    else
+        throw(MooncakeDifferentiateWithError(primal_func, primal_x, primal(y)))
+    end
+
+    return y, pullback
+end
+
+function Mooncake.rrule!!(
+    dw::CoDual{<:DI.DifferentiateWith}, x::CoDual{<:AbstractArray{<:Number}}
+)
+    primal_func = primal(dw)
+    primal_x = primal(x)
+    fdata_arg = x.dx
+    (; f, backend) = primal_func
+    y = zero_fcodual(f(primal_x))
+
+    # output is a vector, so we need to use the vector pullback
+    function pullback_array!!(dy::NoRData)
+        tx = DI.pullback(f, backend, primal_x, (y.dx,))
+        @assert rdata(first(only(tx))) isa rdata_type(tangent_type(typeof(first(primal_x))))
+        fdata_arg .+= only(tx)
+        return NoRData(), dy
+    end
+
+    # output is a scalar, so we can use the scalar pullback
+    function pullback_scalar!!(dy::Number)
+        tx = DI.pullback(f, backend, primal_x, (dy,))
+        @assert rdata(first(only(tx))) isa rdata_type(tangent_type(typeof(first(primal_x))))
+        fdata_arg .+= only(tx)
+        return NoRData(), NoRData()
+    end
+
+    pullback = if primal(y) isa Number
+        pullback_scalar!!
+    elseif primal(y) isa AbstractArray
+        pullback_array!!
+    else
+        throw(MooncakeDifferentiateWithError(primal_func, primal_x, primal(y)))
+    end
+
+    return y, pullback
+end
diff --git a/DifferentiationInterface/src/misc/differentiate_with.jl b/DifferentiationInterface/src/misc/differentiate_with.jl
index 83576c078..256d46f75 100644
--- a/DifferentiationInterface/src/misc/differentiate_with.jl
+++ b/DifferentiationInterface/src/misc/differentiate_with.jl
@@ -13,9 +13,13 @@ Moreover, any larger algorithm `alg` that calls `f2` instead of `f` will also be
 
 !!! warning
     `DifferentiateWith` only supports out-of-place functions `y = f(x)` without additional context arguments.
-    It only makes these functions differentiable if the true backend is either [ForwardDiff](https://github.com/JuliaDiff/ForwardDiff.jl) or automatically importing rules from [ChainRules](https://github.com/JuliaDiff/ChainRules.jl) (e.g. [Zygote](https://github.com/FluxML/Zygote.jl)). Some backends are also able to [manually import rules](https://juliadiff.org/ChainRulesCore.jl/stable/#Packages-supporting-importing-rules-from-ChainRules.) from ChainRules.
+    It only makes these functions differentiable if the true backend is either [ForwardDiff](https://github.com/JuliaDiff/ForwardDiff.jl), [Mooncake](https://github.com/chalk-lab/Mooncake.jl) or automatically importing rules from [ChainRules](https://github.com/JuliaDiff/ChainRules.jl) (e.g. [Zygote](https://github.com/FluxML/Zygote.jl)). Some backends are also able to [manually import rules](https://juliadiff.org/ChainRulesCore.jl/stable/#Packages-supporting-importing-rules-from-ChainRules.) from ChainRules.
     For any other true backend, the differentiation behavior is not altered by `DifferentiateWith` (it becomes a transparent wrapper).
 
+!!! warning
+    When using `DifferentiateWith(f, AutoSomething())`, the function `f` must not close over any active data.
+    As of now, we cannot differentiate with respect to parameters stored inside `f`.
+
 # Fields
 
 - `f`: the function in question, with signature `f(x)`
diff --git a/DifferentiationInterface/test/Back/DifferentiateWith/test.jl b/DifferentiationInterface/test/Back/DifferentiateWith/test.jl
index c8ea57c0b..d2bf57f88 100644
--- a/DifferentiationInterface/test/Back/DifferentiateWith/test.jl
+++ b/DifferentiationInterface/test/Back/DifferentiateWith/test.jl
@@ -1,20 +1,41 @@
 using Pkg
-Pkg.add(["FiniteDiff", "ForwardDiff", "Zygote"])
+Pkg.add(["ChainRulesTestUtils", "FiniteDiff", "ForwardDiff", "Zygote", "Mooncake"])
 
+using ChainRulesTestUtils: ChainRulesTestUtils
 using DifferentiationInterface, DifferentiationInterfaceTest
 import DifferentiationInterfaceTest as DIT
 using FiniteDiff: FiniteDiff
 using ForwardDiff: ForwardDiff
 using Zygote: Zygote
+using Mooncake: Mooncake
+using StableRNGs
 using Test
 
 LOGGING = get(ENV, "CI", "false") == "false"
 
+struct ADBreaker{F}
+    f::F
+end
+
+function (adb::ADBreaker)(x::Number)
+    copyto!(Float64[0], x)  # break ForwardDiff and Zygote
+    return adb.f(x)
+end
+
+function (adb::ADBreaker)(x::AbstractArray)
+    copyto!(similar(x, Float64), x)  # break ForwardDiff and Zygote
+    return adb.f(x)
+end
+
 function differentiatewith_scenarios()
-    bad_scens =  # these closurified scenarios have mutation and type constraints
-        filter(default_scenarios(; include_normal=false, include_closurified=true)) do scen
-            DIT.function_place(scen) == :out
-        end
+    outofplace_scens = filter(DIT.default_scenarios()) do scen
+        DIT.function_place(scen) == :out
+    end
+    # with bad_scens, everything would break
+    bad_scens = map(outofplace_scens) do scen
+        DIT.change_function(scen, ADBreaker(scen.f))
+    end
+    # with good_scens, everything is fixed
     good_scens = map(bad_scens) do scen
         DIT.change_function(scen, DifferentiateWith(scen.f, AutoFiniteDiff()))
     end
@@ -22,8 +43,64 @@ function differentiatewith_scenarios()
 end
 
 test_differentiation(
-    [AutoForwardDiff(), AutoZygote()],
+    [AutoForwardDiff(), AutoZygote(), AutoMooncake(; config=nothing)],
     differentiatewith_scenarios();
     excluded=SECOND_ORDER,
     logging=LOGGING,
+    testset_name="DI tests",
 )
+
+@testset "ChainRules tests" begin
+    @testset for scen in filter(differentiatewith_scenarios()) do scen
+        DIT.operator(scen) == :pullback
+    end
+        ChainRulesTestUtils.test_rrule(scen.f, scen.x; rtol=1e-4)
+    end
+end;
+
+@testset "Mooncake tests" begin
+    @testset for scen in filter(differentiatewith_scenarios()) do scen
+        DIT.operator(scen) == :pullback
+    end
+        Mooncake.TestUtils.test_rule(StableRNG(0), scen.f, scen.x; is_primitive=true)
+    end
+end;
+
+@testset "Mooncake errors" begin
+    MooncakeDifferentiateWithError =
+        Base.get_extension(DifferentiationInterface, :DifferentiationInterfaceMooncakeExt).MooncakeDifferentiateWithError
+
+    e = MooncakeDifferentiateWithError(identity, 1.0, 2.0)
+    @test sprint(showerror, e) ==
+        "MooncakeDifferentiateWithError: For the function type typeof(identity) and input type Float64, the output type Float64 is currently not supported."
+
+    f_num2tup(x::Number) = (x,)
+    f_vec2tup(x::Vector) = (first(x),)
+    f_tup2num(x::Tuple{<:Number}) = only(x)
+    f_tup2vec(x::Tuple{<:Number}) = [only(x)]
+
+    @test_throws MooncakeDifferentiateWithError pullback(
+        DifferentiateWith(f_num2tup, AutoFiniteDiff()),
+        AutoMooncake(; config=nothing),
+        1.0,
+        ((2.0,),),
+    )
+    @test_throws MooncakeDifferentiateWithError pullback(
+        DifferentiateWith(f_vec2tup, AutoFiniteDiff()),
+        AutoMooncake(; config=nothing),
+        [1.0],
+        ((2.0,),),
+    )
+    @test_throws MethodError pullback(
+        DifferentiateWith(f_tup2num, AutoFiniteDiff()),
+        AutoMooncake(; config=nothing),
+        (1.0,),
+        (2.0,),
+    )
+    @test_throws MethodError pullback(
+        DifferentiateWith(f_tup2vec, AutoFiniteDiff()),
+        AutoMooncake(; config=nothing),
+        (1.0,),
+        ([2.0],),
+    )
+end