diff --git a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
index 4efffbcc7..0bdb10497 100644
--- a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
+++ b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
@@ -8,7 +8,7 @@ using MatrixAlgebraKit: ROCSOLVER, LQViaTransposedQR, TruncationStrategy, NoTrun
 using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm, default_eigh_algorithm
 import MatrixAlgebraKit: geqrf!, ungqr!, unmqr!, gesvd!, gesvdj!
 import MatrixAlgebraKit: heevj!, heevd!, heev!, heevx!
-import MatrixAlgebraKit: _sylvester, svd_rank
+import MatrixAlgebraKit: _sylvester, svd_rank, svd_pullback!
 using AMDGPU
 using LinearAlgebra
 using LinearAlgebra: BlasFloat
@@ -185,6 +185,12 @@ function _sylvester(A::AnyROCMatrix, B::AnyROCMatrix, C::AnyROCMatrix)
     return ROCArray(hX)
 end
 
-svd_rank(S::AnyROCVector, rank_atol) = findlast(s -> s ≥ rank_atol, S)
+function svd_rank(S::AnyROCVector; rank_atol = MatrixAlgebraKit.default_pullback_rank_atol(S))
+    return something(findlast(≥(rank_atol), S), 0)
+end
+
+function svd_pullback!(ΔA::AnyROCMatrix, A, USVᴴ, ΔUSVᴴ, ind::AnyROCVector; kwargs...)
+    return svd_pullback!(ΔA, A, USVᴴ, ΔUSVᴴ, collect(ind); kwargs...)
+end
 
 end
diff --git a/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl b/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
index 25a739df0..f9a021644 100644
--- a/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
+++ b/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
@@ -8,7 +8,7 @@ using MatrixAlgebraKit: CUSOLVER, LQViaTransposedQR, TruncationByValue, Abstract
 using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm, default_eig_algorithm, default_eigh_algorithm
 import MatrixAlgebraKit: geqrf!, ungqr!, unmqr!, gesvd!, gesvdp!, gesvdr!, gesvdj!
 import MatrixAlgebraKit: heevj!, heevd!, geev!
-import MatrixAlgebraKit: _gpu_Xgesvdr!, _sylvester, svd_rank
+import MatrixAlgebraKit: _gpu_Xgesvdr!, _sylvester, svd_rank, svd_pullback!
 using CUDA, CUDA.cuBLAS
 using CUDA: i32
 using LinearAlgebra
@@ -197,6 +197,12 @@ function _sylvester(A::AnyCuMatrix, B::AnyCuMatrix, C::AnyCuMatrix)
     return CuArray(hX)
 end
 
-svd_rank(S::AnyCuVector, rank_atol) = findlast(s -> s ≥ rank_atol, S)
+function svd_rank(S::AnyCuVector; rank_atol = MatrixAlgebraKit.default_pullback_rank_atol(S))
+    return something(findlast(≥(rank_atol), S), 0)
+end
+
+function svd_pullback!(ΔA::AnyCuMatrix, A, USVᴴ, ΔUSVᴴ, ind::AnyCuVector; kwargs...)
+    return svd_pullback!(ΔA, A, USVᴴ, ΔUSVᴴ, collect(ind); kwargs...)
+end
 
 end
diff --git a/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl b/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
index a1d5d534d..e2ae96c11 100644
--- a/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
+++ b/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
@@ -15,6 +15,20 @@ using LinearAlgebra
 
 Mooncake.tangent_type(::Type{<:MatrixAlgebraKit.AbstractAlgorithm}) = Mooncake.NoTangent
 
+# needed for GPU tests because Mooncake can't differentiate through CUDA kernels
+@is_primitive Mooncake.DefaultCtx Mooncake.ReverseMode Tuple{typeof(zero!), AbstractArray}
+function Mooncake.rrule!!(::CoDual{typeof(zero!)}, A_dA::CoDual)
+    A, dA = arrayify(A_dA)
+    Ac = copy(A)
+    zero!(A)
+    function zero_adjoint(::NoRData)
+        copy!(A, Ac)
+        zero!(dA)
+        return NoRData(), NoRData()
+    end
+    return A_dA, zero_adjoint
+end
+
 # two-argument in-place factorizations like LQ, QR, EIG
 for (f!, f, pb, adj) in (
         (:qr_full!, :qr_full, :qr_pullback!, :qr_adjoint),
diff --git a/src/pullbacks/svd.jl b/src/pullbacks/svd.jl
index a6e27104a..de1f91fa8 100755
--- a/src/pullbacks/svd.jl
+++ b/src/pullbacks/svd.jl
@@ -85,19 +85,17 @@ function check_and_prepare_svd_cotangents(
     bc = Base.broadcasted(S₁', S₁, aUᴴΔU₁, aVᴴΔV₁) do s₁, s₂, u, v
         return abs(s₁ - s₂) < degeneracy_atol ? u + v : zero(u) + zero(v)
     end
-    Δgauge = max(Δgauge, norm(bc, Inf))
+    Δgauge = max(Δgauge, maximum(abs, bc))
 
     if !iszerotangent(ΔSmat)
         ΔS = diagview(ΔSmat)
         length(indS) == length(ΔS) || throw(DimensionMismatch(lazy"length of selected S values ($(length(indS))) does not match length of ΔS ($(length(ΔS)))"))
+        bad_indS = _ind_intersect((r + 1):length(ΔS), indS)
+        good_indS = _ind_intersect(1:r, indS)
         ΔS₁ = zero(S₁)
-        for (j, i) in enumerate(indS)
-            if i <= r
-                ΔS₁[i] = real(ΔS[j])
-            else
-                Δgauge = max(Δgauge, abs(ΔS[j]))
-            end
-        end
+        ΔS₁[1:length(good_indS)] .= real.(ΔS[good_indS])
+        badΔS₁ = view(ΔS, bad_indS)
+        Δgauge = max(Δgauge, maximum(abs, badΔS₁; init = abs(zero(eltype(ΔS)))))
     else
         ΔS₁ = nothing
     end
diff --git a/test/mooncake/svd.jl b/test/mooncake/svd.jl
index f096fdb8e..2b63198f4 100644
--- a/test/mooncake/svd.jl
+++ b/test/mooncake/svd.jl
@@ -20,4 +20,11 @@ for T in (BLASFloats..., GenericFloats...), n in (17, m, 23)
             TestSuite.test_mooncake_svd(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
         end
     end
+    if T ∈ BLASFloats && CUDA.functional()
+        TestSuite.test_mooncake_svd(CuMatrix{T}, (m, n); atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        if m == n
+            AT = Diagonal{T, CuVector{T}}
+            TestSuite.test_mooncake_svd(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        end
+    end
 end
diff --git a/test/testsuite/enzyme/svd.jl b/test/testsuite/enzyme/svd.jl
index 530663558..2131aa8d5 100644
--- a/test/testsuite/enzyme/svd.jl
+++ b/test/testsuite/enzyme/svd.jl
@@ -69,7 +69,7 @@ function test_enzyme_svd_trunc(
         end
         @testset "trunctol" begin
             S = svd_vals(A, alg)
-            trunc = trunctol(atol = S[1] / 2)
+            trunc = trunctol(atol = maximum(S) / 2)
             truncalg = TruncatedAlgorithm(alg, trunc)
             USVᴴ, _, ΔUSVᴴ, ΔUSVᴴtrunc = ad_svd_trunc_setup(A, truncalg)
             test_reverse(svd_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
diff --git a/test/testsuite/mooncake/svd.jl b/test/testsuite/mooncake/svd.jl
index 23b1d70b0..5ac79744e 100644
--- a/test/testsuite/mooncake/svd.jl
+++ b/test/testsuite/mooncake/svd.jl
@@ -141,7 +141,7 @@ function test_mooncake_svd_trunc(
 
         @testset "trunctol" begin
             S = svd_vals(A)
-            trunc = trunctol(atol = S[1] / 2)
+            trunc = trunctol(atol = maximum(S) / 2)
             alg_trunc = TruncatedAlgorithm(alg, trunc)
 
             USVᴴ, USVᴴtrunc, ΔUSVᴴ_arrays, ΔUSVᴴtrunc_arrays = ad_svd_trunc_setup(A, alg_trunc)