diff --git a/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl b/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
index f834881fd..343bd9681 100644
--- a/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
+++ b/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
@@ -6,6 +6,7 @@ using MatrixAlgebraKit: diagview, inv_safe, truncate
 using MatrixAlgebraKit: qr_pullback!, lq_pullback!
 using MatrixAlgebraKit: qr_null_pullback!, lq_null_pullback!
 using MatrixAlgebraKit: eig_pullback!, eigh_pullback!, eig_vals_pullback!, eigh_vals_pullback!
+using MatrixAlgebraKit: eig_pushforward!, eigh_pushforward!, eig_vals_pushforward!, eigh_vals_pushforward!
 using MatrixAlgebraKit: svd_pullback!, svd_vals_pullback!
 using MatrixAlgebraKit: left_polar_pullback!, right_polar_pullback!
 using MatrixAlgebraKit: left_polar_pushforward!, right_polar_pushforward!
@@ -119,8 +120,10 @@ for (f, pb) in (
 end
 
 for (f, pf) in (
-        (left_polar!, left_polar_pushforward!),
-        (right_polar!, right_polar_pushforward!),
+        (:right_polar!, :right_polar_pushforward!),
+        (:left_polar!, :left_polar_pushforward!),
+        (:eigh_full!, :eigh_pushforward!),
+        (:eig_full!, :eig_pushforward!),
     )
     @eval begin
         function EnzymeRules.forward(
@@ -128,13 +131,17 @@ for (f, pf) in (
                 func::Const{typeof($f)},
                 ::Type{RT},
                 A::Annotation,
-                arg::Annotation{TA},
+                arg::Annotation,
                 alg::Const{<:MatrixAlgebraKit.AbstractAlgorithm},
-            ) where {RT, TA}
+            ) where {RT}
+            A_is_arg1 = !isa(A, Const) && A.val === arg.val[1]
+            A_is_arg2 = !isa(A, Const) && A.val === arg.val[2]
+            A_is_arg = A_is_arg1 || A_is_arg2
             $f(A.val, arg.val, alg.val)
             if !isa(A, Const) && !isa(arg, Const)
                 $pf(A.dval, A.val, arg.val, arg.dval)
             end
+            !A_is_arg && make_zero!(A.dval)
             if EnzymeRules.needs_primal(config) && EnzymeRules.needs_shadow(config)
                 return arg
             elseif EnzymeRules.needs_primal(config)
@@ -367,9 +374,9 @@ for (f, trunc_f, full_f, pb) in (
     end
 end
 
-for (f!, f_full!, pb!) in (
-        (eig_vals!, eig_full!, eig_vals_pullback!),
-        (eigh_vals!, eigh_full!, eigh_vals_pullback!),
+for (f!, f_full!, pb!, pf!) in (
+        (:eig_vals!, :eig_full!, :eig_vals_pullback!, :eig_vals_pushforward!),
+        (:eigh_vals!, :eigh_full!, :eigh_vals_pullback!, :eigh_vals_pushforward!),
     )
     @eval begin
         function EnzymeRules.augmented_primal(
@@ -418,6 +425,34 @@ for (f!, f_full!, pb!) in (
             !isa(D, Const) && !A_is_arg && make_zero!(D.dval)
             return (nothing, nothing, nothing)
         end
+        function EnzymeRules.forward(
+                config::EnzymeRules.FwdConfigWidth{1},
+                func::Const{typeof($f!)},
+                ::Type{RT},
+                A::Annotation{TA},
+                D::Annotation,
+                alg::Const{<:MatrixAlgebraKit.AbstractAlgorithm},
+            ) where {RT, TA}
+            A_is_arg = !isa(A, Const) && TA <: Diagonal && diagview(A.dval) === D.dval
+            DV = $f_full!(A.val, alg.val)
+            Dval, V = DV
+            if !isa(A, Const) && !isa(D, Const)
+                ΔD = A_is_arg ? make_zero(D.dval) : D.dval
+                $pf!(A.dval, A.val, (Diagonal(diagview(Dval)), V), ΔD)
+                A_is_arg && (D.dval .= ΔD)
+            end
+            copyto!(D.val, diagview(Dval))
+            !isa(A, Const) && !A_is_arg && make_zero!(A.dval)
+            if EnzymeRules.needs_primal(config) && EnzymeRules.needs_shadow(config)
+                return D
+            elseif EnzymeRules.needs_primal(config)
+                return D.val
+            elseif EnzymeRules.needs_shadow(config)
+                return D.dval
+            else
+                return nothing
+            end
+        end
     end
 end
 
diff --git a/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl b/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
index 46b4f9538..16241385b 100644
--- a/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
+++ b/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
@@ -7,6 +7,8 @@ using MatrixAlgebraKit: inv_safe, diagview, copy_input, initialize_output, zero!
 using MatrixAlgebraKit: qr_pullback!, lq_pullback!
 using MatrixAlgebraKit: qr_null_pullback!, lq_null_pullback!
 using MatrixAlgebraKit: eig_pullback!, eigh_pullback!, eig_vals_pullback!
+using MatrixAlgebraKit: eig_pushforward!, eig_vals_pushforward!
+using MatrixAlgebraKit: eigh_pushforward!, eigh_vals_pushforward!
 using MatrixAlgebraKit: eig_trunc_pullback!, eigh_trunc_pullback!, eigh_vals_pullback!
 using MatrixAlgebraKit: left_polar_pullback!, right_polar_pullback!
 using MatrixAlgebraKit: left_polar_pushforward!, right_polar_pushforward!
@@ -113,6 +115,8 @@ end
 for (f!, f, pf) in (
         (:left_polar!, :left_polar, :left_polar_pushforward!),
         (:right_polar!, :right_polar, :right_polar_pushforward!),
+        (:eig_full!, :eig_full, :eig_pushforward!),
+        (:eigh_full!, :eigh_full, :eigh_pushforward!),
     )
     @eval begin
         @is_primitive Mooncake.DefaultCtx Mooncake.ForwardMode Tuple{typeof($f!), Any, Tuple{<:Any, <:Any}, MatrixAlgebraKit.AbstractAlgorithm}
@@ -177,12 +181,12 @@ for (f!, f, pb, adj) in (
     end
 end
 
-for (f!, f, f_full, pb, adj) in (
-        (:eig_vals!, :eig_vals, :eig_full, :eig_vals_pullback!, :eig_vals_adjoint),
-        (:eigh_vals!, :eigh_vals, :eigh_full, :eigh_vals_pullback!, :eigh_vals_adjoint),
+for (f!, f, f_full, pb, pf, adj) in (
+        (:eig_vals!, :eig_vals, :eig_full, :eig_vals_pullback!, :eig_vals_pushforward!, :eig_vals_adjoint),
+        (:eigh_vals!, :eigh_vals, :eigh_full, :eigh_vals_pullback!, :eigh_vals_pushforward!, :eigh_vals_adjoint),
     )
     @eval begin
-        @is_primitive Mooncake.DefaultCtx Mooncake.ReverseMode Tuple{typeof($f!), Any, Any, MatrixAlgebraKit.AbstractAlgorithm}
+        @is_primitive Mooncake.DefaultCtx Tuple{typeof($f!), Any, Any, MatrixAlgebraKit.AbstractAlgorithm}
         function Mooncake.rrule!!(::CoDual{typeof($f!)}, A_dA::CoDual, D_dD::CoDual, alg_dalg::CoDual)
             # compute primal
             A, dA = arrayify(A_dA)
@@ -210,7 +214,18 @@ for (f!, f, f_full, pb, adj) in (
             end
             return D_dD, $adj
         end
-        @is_primitive Mooncake.DefaultCtx Mooncake.ReverseMode Tuple{typeof($f), Any, MatrixAlgebraKit.AbstractAlgorithm}
+        function Mooncake.frule!!(::Dual{typeof($f!)}, A_dA::Dual, D_dD::Dual, alg_dalg::Dual)
+            # compute primal
+            A, dA = arrayify(A_dA)
+            D, dD = arrayify(D_dD)
+            # update primal
+            DV = $f_full(A, Mooncake.primal(alg_dalg))
+            V = DV[2]
+            copyto!(D, diagview(DV[1]))
+            $pf(dA, A, (D, V), dD)
+            return D_dD
+        end
+        @is_primitive Mooncake.DefaultCtx Tuple{typeof($f), Any, MatrixAlgebraKit.AbstractAlgorithm}
         function Mooncake.rrule!!(::CoDual{typeof($f)}, A_dA::CoDual, alg_dalg::CoDual)
             # compute primal
             A, dA = arrayify(A_dA)
@@ -227,6 +242,18 @@ for (f!, f, f_full, pb, adj) in (
             end
             return output_codual, $adj
         end
+        function Mooncake.frule!!(::Dual{typeof($f)}, A_dA::Dual, alg_dalg::Dual)
+            # compute primal
+            A, dA = arrayify(A_dA)
+            # update primal
+            DV = $f_full(A, Mooncake.primal(alg_dalg))
+            V = DV[2]
+            output = diagview(DV[1])
+            output_dual = Dual(output, Mooncake.zero_tangent(output))
+            D, dD = arrayify(output_dual)
+            $pf(dA, A, DV, dD)
+            return output_dual
+        end
     end
 end
 
diff --git a/src/MatrixAlgebraKit.jl b/src/MatrixAlgebraKit.jl
index 37b964b44..65de152c4 100644
--- a/src/MatrixAlgebraKit.jl
+++ b/src/MatrixAlgebraKit.jl
@@ -130,6 +130,8 @@ include("pullbacks/svd.jl")
 include("pullbacks/polar.jl")
 
 include("pushforwards/polar.jl")
+include("pushforwards/eig.jl")
+include("pushforwards/eigh.jl")
 
 include("precompile.jl")
 
diff --git a/src/pushforwards/eig.jl b/src/pushforwards/eig.jl
new file mode 100644
index 000000000..9e39f6395
--- /dev/null
+++ b/src/pushforwards/eig.jl
@@ -0,0 +1,22 @@
+function eig_pushforward!(
+        ΔA, A, DV, ΔDV;
+        degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
+    )
+    D, V = DV
+    ΔD, ΔV = ΔDV
+    ΔAV = isnothing(ΔV) ? ΔA * V : mul!(ΔV, ΔA, V) # reusing ΔV memory if possible
+    ∂K = V \ ΔAV
+    if !iszerotangent(ΔD)
+        diagview(ΔD) .= diagview(∂K)
+    end
+    if !iszerotangent(ΔV)
+        ∂K .*= inv_safe.(transpose(diagview(D)) .- diagview(D), degeneracy_atol)
+        mul!(ΔV, V, ∂K, 1, 0)
+    end
+    return ΔDV
+end
+
+function eig_vals_pushforward!(ΔA, A, DV, ΔD; kwargs...)
+    return eig_pushforward!(ΔA, A, DV, (Diagonal(ΔD), nothing); kwargs...)
+end
diff --git a/src/pushforwards/eigh.jl b/src/pushforwards/eigh.jl
new file mode 100644
index 000000000..e610867fe
--- /dev/null
+++ b/src/pushforwards/eigh.jl
@@ -0,0 +1,22 @@
+function eigh_pushforward!(
+        ΔA, A, DV, ΔDV;
+        degeneracy_atol::Real = default_pullback_rank_atol(DV[1]),
+        gauge_atol::Real = default_pullback_gauge_atol(ΔDV[2])
+    )
+    D, V = DV
+    ΔD, ΔV = ΔDV
+    ΔAV = isnothing(ΔV) ? ΔA * V : mul!(ΔV, ΔA, V) # reusing ΔV memory if possible
+    ∂K = V' * ΔAV
+    if !iszerotangent(ΔD)
+        diagview(ΔD) .= real.(diagview(∂K))
+    end
+    if !iszerotangent(ΔV)
+        ∂K .*= inv_safe.(transpose(diagview(D)) .- diagview(D), degeneracy_atol)
+        ΔV = mul!(ΔV, V, ∂K)
+    end
+    return (ΔD, ΔV)
+end
+
+function eigh_vals_pushforward!(ΔA, A, DV, ΔD; kwargs...)
+    return eigh_pushforward!(ΔA, A, DV, (Diagonal(ΔD), nothing); kwargs...)
+end
diff --git a/test/enzyme/eig.jl b/test/enzyme/eig.jl
index 949129eac..1404d751c 100644
--- a/test/enzyme/eig.jl
+++ b/test/enzyme/eig.jl
@@ -16,6 +16,6 @@ for T in (BLASFloats..., GenericFloats...)
     if !is_buildkite
         TestSuite.test_enzyme_eig(T, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
         AT = Diagonal{T, Vector{T}}
-        TestSuite.test_enzyme_eig(AT, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
+        TestSuite.test_enzyme_eig(AT, m; atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
     end
 end
diff --git a/test/enzyme/eigh.jl b/test/enzyme/eigh.jl
index 64c796fc6..05ae7f384 100644
--- a/test/enzyme/eigh.jl
+++ b/test/enzyme/eigh.jl
@@ -14,8 +14,8 @@ m = 19
 for T in (BLASFloats..., GenericFloats...)
     TestSuite.seed_rng!(1234)
     if !is_buildkite
-        #TestSuite.test_enzyme_eigh(T, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
+        TestSuite.test_enzyme_eigh(T, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
         AT = Diagonal{T, Vector{T}}
-        TestSuite.test_enzyme_eigh(AT, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
+        TestSuite.test_enzyme_eigh(AT, m; atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
     end
 end
diff --git a/test/testsuite/enzyme/eig.jl b/test/testsuite/enzyme/eig.jl
index 2c678df3a..b260e557b 100644
--- a/test/testsuite/enzyme/eig.jl
+++ b/test/testsuite/enzyme/eig.jl
@@ -15,38 +15,48 @@ end
 """
     test_enzyme_eig_full(T, sz; rng, atol, rtol)
 
-Test the Enzyme reverse-mode AD rule for `eig_full` and its in-place variant.
+Test the Enzyme foward- and reverse-mode AD rule for `eig_full` and its in-place variant.
 """
 function test_enzyme_eig_full(
         T, sz;
         rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
-    return @testset "eig_full reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
+    return @testset "eig_full: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = make_eig_matrix(T, sz)
         alg = MatrixAlgebraKit.select_algorithm(eig_full, A)
         DV, ΔDV = ad_eig_full_setup(A)
         test_reverse(eig_full, RT, (A, TA), (alg, Const); atol, rtol, output_tangent = ΔDV, fdm)
         test_reverse(call_and_zero!, RT, (eig_full!, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔDV, fdm)
+        if eltype(T) <: Real && T <: Diagonal
+            A = make_eig_matrix(T, sz)
+            test_forward(eig_full, RT, (A, TA), (alg, Const); atol, rtol, fdm)
+            test_forward(call_and_zero!, RT, (eig_full!, Const), (A, TA), (alg, Const); atol, rtol, fdm)
+        end
     end
 end
 
 """
     test_enzyme_eig_vals(T, sz; rng, atol, rtol)
 
-Test the Enzyme reverse-mode AD rule for `eig_vals` and its in-place variant.
+Test the Enzyme forward- and reverse-mode AD rule for `eig_vals` and its in-place variant.
 """
 function test_enzyme_eig_vals(
         T, sz;
         rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
-    return @testset "eig_vals reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
+    return @testset "eig_vals: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = make_eig_matrix(T, sz)
         alg = MatrixAlgebraKit.select_algorithm(eig_vals, A)
         D, ΔD = ad_eig_vals_setup(A)
         test_reverse(eig_vals, RT, (A, TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
         test_reverse(call_and_zero!, RT, (eig_vals!, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
+        if eltype(T) <: Real
+            A = make_eig_matrix(T, sz)
+            test_forward(eig_vals, RT, (A, TA), (alg, Const); atol, rtol, fdm)
+            test_forward(call_and_zero!, RT, (eig_vals!, Const), (A, TA), (alg, Const); atol, rtol, fdm)
+        end
     end
 end
 
diff --git a/test/testsuite/enzyme/eigh.jl b/test/testsuite/enzyme/eigh.jl
index 73dc84ed2..83c81296d 100644
--- a/test/testsuite/enzyme/eigh.jl
+++ b/test/testsuite/enzyme/eigh.jl
@@ -15,38 +15,46 @@ end
 """
     test_enzyme_eigh_full(T, sz; rng, atol, rtol)
 
-Test the Enzyme reverse-mode AD rule for `eigh_full` and its in-place variant.
+Test the Enzyme forward- and reverse-mode AD rule for `eigh_full` and its in-place variant.
 """
 function test_enzyme_eigh_full(
         T, sz;
         rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
-    return @testset "eigh_full reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
+    return @testset "eigh_full: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = make_eigh_matrix(T, sz)
         alg = MatrixAlgebraKit.select_algorithm(eigh_full, A)
         DV, ΔDV = ad_eigh_full_setup(A)
         test_reverse(eigh_wrapper, RT, (eigh_full, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔDV, fdm)
         test_reverse(eigh!_wrapper, RT, (eigh_full!, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔDV, fdm)
+        if eltype(T) <: Real
+            A = make_eigh_matrix(T, sz)
+            test_forward(eigh_wrapper, RT, (eigh_full, Const), (A, TA), (alg, Const); atol, rtol, fdm)
+            test_forward(eigh!_wrapper, RT, (eigh_full!, Const), (A, TA), (alg, Const); atol, rtol, fdm)
+        end
     end
 end
 
 """
     test_enzyme_eigh_vals(T, sz; rng, atol, rtol)
 
-Test the Enzyme reverse-mode AD rule for `eigh_vals` and its in-place variant.
+Test the Enzyme forward- and reverse-mode AD rule for `eigh_vals` and its in-place variant.
 """
 function test_enzyme_eigh_vals(
         T, sz;
         rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
-    return @testset "eigh_vals reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
+    return @testset "eigh_vals: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = make_eigh_matrix(T, sz)
         alg = MatrixAlgebraKit.select_algorithm(eigh_vals, A)
         D, ΔD = ad_eigh_vals_setup(A)
         test_reverse(eigh_wrapper, RT, (eigh_vals, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
         test_reverse(eigh!_wrapper, RT, (eigh_vals!, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
+        A = make_eigh_matrix(T, sz)
+        test_forward(eigh_wrapper, RT, (eigh_vals, Const), (A, TA), (alg, Const); atol, rtol, fdm)
+        test_forward(eigh!_wrapper, RT, (eigh_vals!, Const), (A, TA), (alg, Const); atol, rtol, fdm)
     end
 end
 
diff --git a/test/testsuite/mooncake/eig.jl b/test/testsuite/mooncake/eig.jl
index aad4b4881..3cc0063c7 100644
--- a/test/testsuite/mooncake/eig.jl
+++ b/test/testsuite/mooncake/eig.jl
@@ -15,7 +15,7 @@ end
 """
     test_mooncake_eig_full(T, sz; rng, atol, rtol)
 
-Test the Mooncake reverse-mode AD rule for `eig_full` and its in-place variant.
+Test the Mooncake forward- and reverse-mode AD rule for `eig_full` and its in-place variant.
 """
 function test_mooncake_eig_full(
         T, sz;
@@ -29,25 +29,39 @@ function test_mooncake_eig_full(
 
         Mooncake.TestUtils.test_rule(
             rng, eig_full, A, alg;
-            mode = Mooncake.ReverseMode, output_tangent, atol, rtol
+            mode = Mooncake.ReverseMode,
+            output_tangent, atol, rtol
         )
+        Mooncake.TestUtils.test_rule(
+            rng, call_and_zero!, eig_full!, A, alg;
+            mode = Mooncake.ReverseMode,
+            output_tangent, atol, rtol, is_primitive = false
+        )
+        if !(eltype(T) <: ComplexF64)
+            Mooncake.TestUtils.test_rule(
+                rng, eig_full, A, alg;
+                mode = Mooncake.ForwardMode,
+                atol, rtol
+            )
+            Mooncake.TestUtils.test_rule(
+                rng, call_and_zero!, eig_full!, A, alg;
+                mode = Mooncake.ForwardMode,
+                atol, rtol, is_primitive = false
+            )
+        end
         if T <: Diagonal{<:Complex}
             Mooncake.TestUtils.test_rule(
                 rng, eig_full!, A, (A, DV[2]), alg;
-                mode = Mooncake.ReverseMode, output_tangent, atol, rtol
+                output_tangent, atol, rtol
             )
         end
-        Mooncake.TestUtils.test_rule(
-            rng, call_and_zero!, eig_full!, A, alg;
-            mode = Mooncake.ReverseMode, output_tangent, atol, rtol, is_primitive = false
-        )
     end
 end
 
 """
     test_mooncake_eig_vals(T, sz; rng, atol, rtol)
 
-Test the Mooncake reverse-mode AD rule for `eig_vals` and its in-place variant.
+Test the Mooncake forward- and reverse-mode AD rule for `eig_vals` and its in-place variant.
 """
 function test_mooncake_eig_vals(
         T, sz;
@@ -61,17 +75,17 @@ function test_mooncake_eig_vals(
 
         Mooncake.TestUtils.test_rule(
             rng, eig_vals, A, alg;
-            mode = Mooncake.ReverseMode, output_tangent, atol, rtol
+            output_tangent, atol, rtol
         )
         if T <: Diagonal{<:Complex}
             Mooncake.TestUtils.test_rule(
                 rng, eig_vals!, A, A.diag, alg;
-                mode = Mooncake.ReverseMode, output_tangent, atol, rtol
+                output_tangent, atol, rtol
             )
         end
         Mooncake.TestUtils.test_rule(
             rng, call_and_zero!, eig_vals!, A, alg;
-            mode = Mooncake.ReverseMode, output_tangent, atol, rtol, is_primitive = false
+            output_tangent, atol, rtol, is_primitive = false
         )
     end
 end
diff --git a/test/testsuite/mooncake/eigh.jl b/test/testsuite/mooncake/eigh.jl
index 62952aa8e..00f29a6f7 100644
--- a/test/testsuite/mooncake/eigh.jl
+++ b/test/testsuite/mooncake/eigh.jl
@@ -35,6 +35,16 @@ function test_mooncake_eigh_full(
             rng, eigh!_wrapper, eigh_full!, A, alg;
             mode = Mooncake.ReverseMode, output_tangent, is_primitive = false, atol, rtol
         )
+        if !(eltype(T) <: Complex)
+            Mooncake.TestUtils.test_rule(
+                rng, eigh_wrapper, eigh_full, A, alg;
+                mode = Mooncake.ForwardMode, output_tangent, is_primitive = false, atol, rtol
+            )
+            Mooncake.TestUtils.test_rule(
+                rng, eigh!_wrapper, eigh_full!, A, alg;
+                mode = Mooncake.ForwardMode, output_tangent, is_primitive = false, atol, rtol
+            )
+        end
     end
 end
 
@@ -55,11 +65,11 @@ function test_mooncake_eigh_vals(
 
         Mooncake.TestUtils.test_rule(
             rng, eigh_wrapper, eigh_vals, A, alg;
-            mode = Mooncake.ReverseMode, output_tangent, is_primitive = false, atol, rtol
+            output_tangent, is_primitive = false, atol, rtol
         )
         Mooncake.TestUtils.test_rule(
             rng, eigh!_wrapper, eigh_vals!, A, alg;
-            mode = Mooncake.ReverseMode, output_tangent, is_primitive = false, atol, rtol
+            output_tangent, is_primitive = false, atol, rtol
         )
     end
 end