diff --git a/Project.toml b/Project.toml
index 0d680594..9bf9cd24 100644
--- a/Project.toml
+++ b/Project.toml
@@ -84,10 +84,10 @@ Interpolations = "0.15"
 JSON3 = "1"
 KernelDensityEstimate = "0.5.6"
 LinearAlgebra = "1.10"
-ManifoldDiff = "0.3"
+ManifoldDiff = "0.3, 0.4"
 Manifolds = "0.10"
 ManifoldsBase = "0.15"
-Manopt = "0.4.40, 0.5"
+Manopt = "^0.5.3"
 MetaGraphs = "0.7, 0.8"
 Optim = "1"
 OrderedCollections = "1"
diff --git a/src/parametric/services/ParametricOptim.jl b/src/parametric/services/ParametricOptim.jl
index b203c084..17033fd8 100644
--- a/src/parametric/services/ParametricOptim.jl
+++ b/src/parametric/services/ParametricOptim.jl
@@ -8,7 +8,11 @@ function optimizeManifold_FD(
 )
   # finitediff setup
   r_backend = ManifoldDiff.TangentDiffBackend(
-    ManifoldDiff.FiniteDifferencesBackend()
+    if v"0.4" <=  pkgversion(ManifoldDiff)
+      ManifoldDiff.AutoFiniteDifferences(central_fdm(5, 1))
+    else
+      ManifoldDiff.FiniteDifferencesBackend()
+    end
   )
   
   ## finitediff gradient (non-manual)
diff --git a/src/services/FactorGradients.jl b/src/services/FactorGradients.jl
index 6bee605d..f8e67f54 100644
--- a/src/services/FactorGradients.jl
+++ b/src/services/FactorGradients.jl
@@ -6,7 +6,13 @@ function factorJacobian(
   fg,
   faclabel::Symbol,
   p0 = ArrayPartition(first.(getVal.(fg, getVariableOrder(fg, faclabel), solveKey = :parametric))...),
-  backend = ManifoldDiff.TangentDiffBackend(ManifoldDiff.FiniteDiffBackend()),
+  backend = ManifoldDiff.TangentDiffBackend(
+    if v"0.4" <=  pkgversion(ManifoldDiff)
+      ManifoldDiff.AutoFiniteDifferences(central_fdm(5, 1))
+    else
+      ManifoldDiff.FiniteDifferencesBackend()
+    end
+  )
 )
 
   fac = getFactor(fg, faclabel)
diff --git a/test/manifolds/factordiff.jl b/test/manifolds/factordiff.jl
index a870559c..d1df6118 100644
--- a/test/manifolds/factordiff.jl
+++ b/test/manifolds/factordiff.jl
@@ -97,11 +97,15 @@ function resid_SE2(X, p, q)
 end
 
 
+# finitediff setup
 # finitediff setup
 r_backend = ManifoldDiff.TangentDiffBackend(
-  ManifoldDiff.FiniteDifferencesBackend()
+  if v"0.4" <=  pkgversion(ManifoldDiff)
+    ManifoldDiff.AutoFiniteDifferences(central_fdm(5, 1))
+  else
+    ManifoldDiff.FiniteDifferencesBackend()
+  end
 )
-
 Me = Euclidean(3)
 
 function _factorJac!(J, z, p1, p2)
@@ -123,9 +127,15 @@ J_ = _factorJac!(J, z, p1, p2)
 # @profview _factorJac!(J, z, p1, p2)
 
 if false
+  # finitediff setup
   z_backend = ManifoldDiff.TangentDiffBackend(
-    ManifoldDiff.ZygoteDiffBackend()
+    if v"0.4" <=  pkgversion(ManifoldDiff)
+      ManifoldDiff.AutoFiniteDifferences(central_fdm(5, 1))
+    else
+      ManifoldDiff.FiniteDifferencesBackend()
+    end
   )
+
   g = ManifoldDiff.jacobian(M, Euclidean(3), f_SE2_x0, p1, z_backend)
 else
   @info "ManifoldDiff.ZygoteDiffBackend usage still under development (23Q3)"
diff --git a/test/manifolds/manifolddiff.jl b/test/manifolds/manifolddiff.jl
index 71b0035e..2e6e0591 100644
--- a/test/manifolds/manifolddiff.jl
+++ b/test/manifolds/manifolddiff.jl
@@ -13,7 +13,11 @@ import Rotations as _Rot
 
 # finitediff setup
 r_backend = ManifoldDiff.TangentDiffBackend(
+  if v"0.4" <=  pkgversion(ManifoldDiff)
+    ManifoldDiff.AutoFiniteDifferences(central_fdm(5, 1))
+  else
     ManifoldDiff.FiniteDifferencesBackend()
+  end
 )
 
 ##