diff --git a/src/algorithms/optimization/implicit_differentiation.jl b/src/algorithms/optimization/implicit_differentiation.jl
index 6c7fd4e5c..f00632504 100644
--- a/src/algorithms/optimization/implicit_differentiation.jl
+++ b/src/algorithms/optimization/implicit_differentiation.jl
@@ -55,6 +55,10 @@ function GradientAlgorithm(;
     return alg_type(solver)
 end
 
+# a `GradientAlgorithm` has no top-level `tol` field (it lives on `solver_alg`), so the
+# default `MPSKit.DynamicTols._updatetol` (which sets `alg.tol`) doesn't apply
+_updatetol(alg::GradientAlgorithm, tol::Real) = @set alg.solver_alg.tol = tol
+
 #
 # Fixed-point gradient computation
 #
@@ -95,10 +99,6 @@ end
 FixedPointGradient(; kwargs...) = GradientAlgorithm(; alg = :FixedPointGradient, kwargs...)
 GRADIENT_ALGORITHM_SYMBOLS[:FixedPointGradient] = FixedPointGradient
 
-# `FixedPointGradient` has no top-level `tol` field (it lives on `solver_alg`), so the
-# default `MPSKit.DynamicTols._updatetol` (which sets `alg.tol`) doesn't apply
-_updatetol(alg::FixedPointGradient, tol::Real) = @set alg.solver_alg.tol = tol
-
 const FIXEDPOINT_SOLVER_SYMBOLS = IdDict{Symbol, Type{<:Any}}(
     :GMRES => GMRES, :BiCGStab => BiCGStab, :Arnoldi => Arnoldi,
 )
diff --git a/src/environments/ctmrg_environments.jl b/src/environments/ctmrg_environments.jl
index cabc0e764..ac1ee525e 100644
--- a/src/environments/ctmrg_environments.jl
+++ b/src/environments/ctmrg_environments.jl
@@ -328,6 +328,17 @@ function update!(env::CTMRGEnv{C, T}, env´::CTMRGEnv{C, T}) where {C, T}
     env.edges .= env´.edges
     return env
 end
+# patch for the case where the corners are of a different type, which happens when running
+# variational optimization using an implicit gradient
+function update!(env::CTMRGEnv{C, T}, env´::CTMRGEnv{C´, T}) where {C, C´, T}
+    env.corners .= _convert_cornertype.(C, env´.corners)
+    env.edges .= env´.edges
+    return env
+end
+function _convert_cornertype(::Type{C}, c) where {C <: DiagonalTensorMap}
+    d = DiagonalTensorMap(c)
+    return scalartype(C) <: Real ? real(d) : d
+end
 
 # Rotate corners & edges counter-clockwise
 function Base.rotl90(env::CTMRGEnv{C, T}) where {C, T}
diff --git a/test/examples/heisenberg.jl b/test/examples/heisenberg.jl
index 8441998f6..d6fd28e54 100644
--- a/test/examples/heisenberg.jl
+++ b/test/examples/heisenberg.jl
@@ -52,8 +52,8 @@ end
     @test all(@. ξ_h > 0 && ξ_v > 0)
 end
 
-@testset "C4v AD optimization with scalartype T=$T and projector_alg=$projector_alg" for (T, projector_alg) in
-    Iterators.product([Float64, ComplexF64], [:C4vEighProjector, :C4vQRProjector])
+@testset "C4v AD optimization with scalartype T=$T, projector_alg=$projector_alg and gradient_alg=$gradient_alg" for (T, projector_alg, gradient_alg) in
+    Iterators.product([Float64, ComplexF64], [:C4vEighProjector, :C4vQRProjector], [:FixedPointGradient, :ImplicitGradient])
     # initialize symmetric states
     Random.seed!(123456789)
     symm = RotateReflect()
@@ -69,6 +69,7 @@ end
         H, peps₀, env₀;
         optimizer_alg = (; tol = gradtol, maxiter = 25),
         boundary_alg = (; alg = :C4vCTMRG, projector_alg, maxiter = 500),
+        gradient_alg = (; alg = gradient_alg),
     )
     ξ_h, ξ_v, = correlation_length(peps, env)
     @info "Optimized energy = $E."