diff --git a/Project.toml b/Project.toml
index 4344242d5..04eb90c2c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -48,7 +48,7 @@ Adapt = "4"
 CUDA = "6"
 ChainRulesCore = "1"
 Dictionaries = "0.4"
-Enzyme = "0.13.157"
+Enzyme = "0.13.183"
 EnzymeTestUtils = "0.2.8"
 FiniteDifferences = "0.12"
 GPUArrays = "11.4.1"
diff --git a/ext/TensorKitEnzymeExt/TensorKitEnzymeExt.jl b/ext/TensorKitEnzymeExt/TensorKitEnzymeExt.jl
index cadae496a..2095b3c52 100644
--- a/ext/TensorKitEnzymeExt/TensorKitEnzymeExt.jl
+++ b/ext/TensorKitEnzymeExt/TensorKitEnzymeExt.jl
@@ -15,5 +15,6 @@ include("utility.jl")
 include("linalg.jl")
 include("indexmanipulations.jl")
 include("tensoroperations.jl")
+include("factorizations.jl")
 
 end
diff --git a/ext/TensorKitEnzymeExt/factorizations.jl b/ext/TensorKitEnzymeExt/factorizations.jl
new file mode 100644
index 000000000..4e6b6e962
--- /dev/null
+++ b/ext/TensorKitEnzymeExt/factorizations.jl
@@ -0,0 +1,69 @@
+# need these due to Enzyme choking on blocks
+
+for f in (:project_hermitian, :project_antihermitian)
+    f! = Symbol(f, :!)
+    @eval begin
+        function EnzymeRules.augmented_primal(
+                config::EnzymeRules.RevConfigWidth{1},
+                func::Const{typeof($f!)},
+                ::Type{RT},
+                A::Annotation{<:AbstractTensorMap},
+                arg::Annotation{<:AbstractTensorMap},
+                alg::Const,
+            ) where {RT}
+            $f!(A.val, arg.val, alg.val)
+            primal = EnzymeRules.needs_primal(config) ? arg.val : nothing
+            shadow = EnzymeRules.needs_shadow(config) ? arg.dval : nothing
+            cache = nothing
+            return EnzymeRules.AugmentedReturn(primal, shadow, cache)
+        end
+        function EnzymeRules.reverse(
+                config::EnzymeRules.RevConfigWidth{1},
+                func::Const{typeof($f!)},
+                ::Type{RT},
+                cache,
+                A::Annotation{<:AbstractTensorMap},
+                arg::Annotation{<:AbstractTensorMap},
+                alg::Const,
+            ) where {RT}
+            if !isa(A, Const) && !isa(arg, Const)
+                $f!(arg.dval, arg.dval, alg.val)
+                if A.dval !== arg.dval
+                    A.dval .+= arg.dval
+                    make_zero!(arg.dval)
+                end
+            end
+            return (nothing, nothing, nothing)
+        end
+        function EnzymeRules.augmented_primal(
+                config::EnzymeRules.RevConfigWidth{1},
+                func::Const{typeof($f)},
+                ::Type{RT},
+                A::Annotation{<:AbstractTensorMap},
+                alg::Const,
+            ) where {RT}
+            ret = $f(A.val, alg.val)
+            dret = make_zero(ret)
+            primal = EnzymeRules.needs_primal(config) ? ret : nothing
+            shadow = EnzymeRules.needs_shadow(config) ? dret : nothing
+            cache = dret
+            return EnzymeRules.AugmentedReturn(primal, shadow, cache)
+        end
+        function EnzymeRules.reverse(
+                config::EnzymeRules.RevConfigWidth{1},
+                func::Const{typeof($f)},
+                ::Type{RT},
+                cache,
+                A::Annotation{<:AbstractTensorMap},
+                alg::Const,
+            ) where {RT}
+            dret = cache
+            if !isa(A, Const)
+                $f!(dret, dret, alg.val)
+                add!(A.dval, dret)
+            end
+            make_zero!(dret)
+            return (nothing, nothing)
+        end
+    end
+end
diff --git a/ext/TensorKitEnzymeExt/utility.jl b/ext/TensorKitEnzymeExt/utility.jl
index dd99d96e8..d03848c81 100644
--- a/ext/TensorKitEnzymeExt/utility.jl
+++ b/ext/TensorKitEnzymeExt/utility.jl
@@ -135,6 +135,7 @@ end
 @inline EnzymeRules.inactive(::typeof(TensorKit.insertleftunit), ::HomSpace, ::Any) = nothing
 @inline EnzymeRules.inactive(::typeof(TensorKit.insertrightunit), ::HomSpace, ::Any) = nothing
 @inline EnzymeRules.inactive(::typeof(TensorKit.removeunit), ::HomSpace, ::Any) = nothing
+@inline EnzymeRules.inactive(::typeof(TensorKit.infimum), ::Any, ::Any) = nothing
 @inline EnzymeRules.inactive(::typeof(TensorKit.sectorstructure), ::Any) = nothing
 @inline EnzymeRules.inactive(::typeof(TensorKit.degeneracystructure), ::Any) = nothing
 @inline EnzymeRules.inactive(::typeof(TensorKit.select), s::HomSpace, i::Index2Tuple) = nothing
diff --git a/src/factorizations/diagonal.jl b/src/factorizations/diagonal.jl
index dae550ea1..49261f24e 100644
--- a/src/factorizations/diagonal.jl
+++ b/src/factorizations/diagonal.jl
@@ -3,6 +3,7 @@
 _repack_diagonal(d::DiagonalTensorMap) = Diagonal(d.data)
 _repack_diagonal(d::SectorVector) = Diagonal(parent(d))
 
+MAK.diagonal(t::SectorVector) = DiagonalTensorMap(t)
 MAK.diagview(t::DiagonalTensorMap) = SectorVector(t.data, TensorKit.diagonalblockstructure(space(t)))
 
 for f in (
diff --git a/src/factorizations/pullbacks.jl b/src/factorizations/pullbacks.jl
index b910a184c..72ad94008 100644
--- a/src/factorizations/pullbacks.jl
+++ b/src/factorizations/pullbacks.jl
@@ -11,6 +11,16 @@ for pullback! in (
         end
         return Δt
     end
+    @eval function MAK.$pullback!(
+            Δt::AbstractTensorMap, ::Nothing, F, ΔF; kwargs...
+        )
+        foreachblock(Δt) do c, (Δb,)
+            Fc = block.(F, Ref(c))
+            ΔFc = block.(ΔF, Ref(c))
+            return MAK.$pullback!(Δb, nothing, Fc, ΔFc; kwargs...)
+        end
+        return Δt
+    end
 end
 for pullback! in (:qr_null_pullback!, :lq_null_pullback!)
     @eval function MAK.$pullback!(
@@ -41,6 +51,33 @@ for pullback! in (:svd_pullback!, :eig_pullback!, :eigh_pullback!)
         end
         return Δt
     end
+    @eval function MAK.$pullback!(
+            Δt::AbstractTensorMap, ::Nothing, F, ΔF, inds; kwargs...
+        )
+        foreachblock(Δt) do c, (Δb,)
+            haskey(inds, c) || return nothing
+            ind = inds[c]
+            Fc = block.(F, Ref(c))
+            ΔFc = map(ΔFc -> isnothing(ΔFc) ? nothing : block(ΔFc, c), ΔF)
+            return MAK.$pullback!(Δb, nothing, Fc, ΔFc, ind; kwargs...)
+        end
+        return Δt
+    end
+    @eval function MAK.$pullback!(
+            Δt::AbstractTensorMap, t::AbstractTensorMap, F, ΔF, ::Colon; kwargs...
+        )
+        return MAK.$pullback!(Δt, t, F, ΔF, _notrunc_ind(t); kwargs...)
+    end
+    @eval function MAK.$pullback!(
+            Δt::AbstractTensorMap, ::Nothing, F, ΔF; kwargs...
+        )
+        return MAK.$pullback!(Δt, nothing, F, ΔF, _notrunc_ind(Δt); kwargs...)
+    end
+    @eval function MAK.$pullback!(
+            Δt::AbstractTensorMap, ::Nothing, F, ΔF, ::Colon; kwargs...
+        )
+        return MAK.$pullback!(Δt, nothing, F, ΔF, _notrunc_ind(Δt); kwargs...)
+    end
 end
 
 for pullback_trunc! in (:svd_trunc_pullback!, :eig_trunc_pullback!, :eigh_trunc_pullback!)
@@ -97,3 +134,7 @@ function MAK.remove_svd_gauge_dependence!(
     end
     return ΔU, ΔVᴴ
 end
+
+MAK.has_equal_storage(A::AbstractTensorMap, B::AbstractTensorMap) = A === B
+MAK.has_equal_storage(A::AbstractTensorMap, B::SectorVector) = false
+MAK.has_equal_storage(A::SectorVector, B::AbstractTensorMap) = false
diff --git a/test/enzyme-factorizations/factorizations.jl b/test/enzyme-factorizations/factorizations.jl
new file mode 100644
index 000000000..d2f4e66ef
--- /dev/null
+++ b/test/enzyme-factorizations/factorizations.jl
@@ -0,0 +1,123 @@
+using Test, TestExtras
+using TensorKit
+using TensorOperations
+using MatrixAlgebraKit
+using MatrixAlgebraKit: remove_svd_gauge_dependence!
+using MatrixAlgebraKit: remove_eig_gauge_dependence!
+using MatrixAlgebraKit: remove_eigh_gauge_dependence!
+using MatrixAlgebraKit: remove_lq_gauge_dependence!, remove_lq_null_gauge_dependence!
+using MatrixAlgebraKit: remove_qr_gauge_dependence!, remove_qr_null_gauge_dependence!
+using Enzyme, EnzymeTestUtils
+using Random
+
+spacelist = ad_spacelist(fast_tests)
+eltypes = (Float64, ComplexF64)
+
+@timedtestset "Enzyme - Factorizations: $(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes, t in (randn(T, V[1] ⊗ V[2] ← V[1] ⊗ V[2]), randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])'))
+    atol = default_tol(T)
+    rtol = default_tol(T)
+
+    @testset "SVD" begin
+        S = svd_vals(t)
+        EnzymeTestUtils.test_reverse(svd_vals, Duplicated, (t, Duplicated); atol, rtol)
+
+        USVᴴ = svd_full(t)
+        ΔUSVᴴ = EnzymeTestUtils.rand_tangent(USVᴴ)
+        remove_svd_gauge_dependence!(ΔUSVᴴ[1], ΔUSVᴴ[3], USVᴴ...)
+        EnzymeTestUtils.test_reverse(svd_full, Duplicated, (t, Duplicated); output_tangent = ΔUSVᴴ, atol, rtol)
+
+        USVᴴ = svd_compact(t)
+        ΔUSVᴴ = EnzymeTestUtils.rand_tangent(USVᴴ)
+        remove_svd_gauge_dependence!(ΔUSVᴴ[1], ΔUSVᴴ[3], USVᴴ...)
+        EnzymeTestUtils.test_reverse(svd_compact, Duplicated, (t, Duplicated); output_tangent = ΔUSVᴴ, atol, rtol)
+
+        V_trunc = spacetype(t)(c => min(size(b)...) ÷ 2 for (c, b) in blocks(t))
+        trunc = truncspace(V_trunc)
+        alg = MatrixAlgebraKit.select_algorithm(svd_trunc_no_error, t, nothing; trunc)
+        USVᴴtrunc = svd_trunc_no_error(t, alg)
+        ΔUSVᴴtrunc = EnzymeTestUtils.rand_tangent(USVᴴtrunc)
+        remove_svd_gauge_dependence!(ΔUSVᴴtrunc[1], ΔUSVᴴtrunc[3], USVᴴtrunc...)
+        EnzymeTestUtils.test_reverse(svd_trunc_no_error, Duplicated, (t, Duplicated), (alg, Const); output_tangent = ΔUSVᴴtrunc, atol, rtol)
+    end
+
+    @testset "LQ" begin
+        EnzymeTestUtils.test_reverse(lq_compact, Duplicated, (t, Duplicated); atol, rtol)
+
+        # lq_full/lq_null requires being careful with gauges
+        LQ = lq_full(t)
+        ΔLQ = EnzymeTestUtils.rand_tangent(LQ)
+        remove_lq_gauge_dependence!(ΔLQ..., t, LQ...)
+        EnzymeTestUtils.test_reverse(lq_full, Duplicated, (t, Duplicated); output_tangent = ΔLQ, atol, rtol)
+
+        Nᴴ = lq_null(t)
+        Q = lq_compact(t)[2]
+        ΔNᴴ = EnzymeTestUtils.rand_tangent(Nᴴ)
+        remove_lq_null_gauge_dependence!(ΔNᴴ, Q, Nᴴ)
+        EnzymeTestUtils.test_reverse(lq_null, Duplicated, (t, Duplicated); output_tangent = ΔNᴴ, atol, rtol)
+    end
+
+    @testset "QR" begin
+        # qr_full/qr_null requires being careful with gauges
+        QR = qr_full(t)
+        ΔQR = EnzymeTestUtils.rand_tangent(QR)
+        remove_qr_gauge_dependence!(ΔQR..., t, QR...)
+        EnzymeTestUtils.test_reverse(qr_full, Duplicated, (t, Duplicated); output_tangent = ΔQR, atol, rtol)
+
+        N = qr_null(t)
+        Q = qr_compact(t)[1]
+        ΔN = EnzymeTestUtils.rand_tangent(N)
+        remove_qr_null_gauge_dependence!(ΔN, t, N)
+        EnzymeTestUtils.test_reverse(qr_null, Duplicated, (t, Duplicated); atol, rtol, output_tangent = ΔN)
+    end
+end
+
+@timedtestset "Enzyme - Factorizations (EIGH/EIG): $(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes, t in (randn(T, V[1] ← V[1]), rand(T, V[1] ⊗ V[2] ← V[1] ⊗ V[2]))
+    atol = default_tol(T)
+    rtol = default_tol(T)
+
+    @testset "EIG" begin
+        DV = eig_full(t)
+        ΔDV = EnzymeTestUtils.rand_tangent(DV)
+        remove_eig_gauge_dependence!(ΔDV[2], DV...)
+        EnzymeTestUtils.test_reverse(eig_full, Duplicated, (t, Duplicated); output_tangent = ΔDV, atol, rtol)
+
+        D = eig_vals(t)
+        EnzymeTestUtils.test_reverse(eig_vals, Duplicated, (t, Duplicated); atol, rtol)
+
+        V_trunc = spacetype(t)(c => min(size(b)...) ÷ 2 for (c, b) in blocks(t))
+        trunc = truncspace(V_trunc)
+        alg = MatrixAlgebraKit.select_algorithm(eig_trunc_no_error, t, nothing; trunc)
+        DVtrunc = eig_trunc_no_error(t, alg)
+        ΔDVtrunc = EnzymeTestUtils.rand_tangent(DVtrunc)
+        remove_eig_gauge_dependence!(ΔDVtrunc[2], DVtrunc...)
+        EnzymeTestUtils.test_reverse(eig_trunc_no_error, Duplicated, (t, Duplicated), (alg, Const); output_tangent = ΔDVtrunc, atol, rtol)
+    end
+
+    @testset "EIGH" begin
+        th = project_hermitian(t)
+        DV = eigh_full(th)
+        ΔDV = EnzymeTestUtils.rand_tangent(DV)
+        remove_eigh_gauge_dependence!(ΔDV[2], DV...)
+        proj_eigh_full(t) = eigh_full(project_hermitian(t))
+        EnzymeTestUtils.test_reverse(proj_eigh_full, Duplicated, (th, Duplicated); output_tangent = ΔDV, atol, rtol)
+
+        D = eigh_vals(th)
+        EnzymeTestUtils.test_reverse(eigh_vals ∘ project_hermitian, Duplicated, (th, Duplicated); atol, rtol)
+
+        V_trunc = spacetype(th)(c => min(size(b)...) ÷ 2 for (c, b) in blocks(t))
+        trunc = truncspace(V_trunc)
+        alg = MatrixAlgebraKit.select_algorithm(eigh_trunc_no_error, th, nothing; trunc)
+        DVtrunc = eigh_trunc_no_error(th, alg)
+        ΔDVtrunc = EnzymeTestUtils.rand_tangent(DVtrunc)
+        remove_eigh_gauge_dependence!(ΔDVtrunc[2], DVtrunc...)
+        proj_eigh(t, alg) = eigh_trunc_no_error(project_hermitian(t), alg)
+        EnzymeTestUtils.test_reverse(proj_eigh, Duplicated, (th, Duplicated), (alg, Const); output_tangent = ΔDVtrunc, atol, rtol)
+    end
+
+    @testset "Projections" begin
+        EnzymeTestUtils.test_reverse(project_hermitian, Duplicated, (t, Duplicated); atol, rtol)
+        EnzymeTestUtils.test_reverse(project_antihermitian, Duplicated, (t, Duplicated); atol, rtol)
+        EnzymeTestUtils.test_reverse(project_hermitian!, Duplicated, (t, Duplicated); atol, rtol)
+        EnzymeTestUtils.test_reverse(project_antihermitian!, Duplicated, (t, Duplicated); atol, rtol)
+    end
+end