diff --git a/NEWS.md b/NEWS.md
index 764d10b9..b4c1f585 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -23,6 +23,7 @@ The list below highlights breaking changes according to normal semver workflow -
 - Further bug fixes for transition to `StaticArrays` value stores and computes, including `Position{N}` (#1779, #1776).
 - Restore `DifferentialEquation.jl` factor `DERelative` functionality and tests that were suppressed in a previous upgrade (#1774, #1777).
 - Restore previously suppressed tests (#1781, #1721, #1780)
+- Improve DERelative factor on-manifold operations (#1775, #1802, #1803).
 
 # Changes in v0.34
 
diff --git a/Project.toml b/Project.toml
index 1e150c45..8d5b52fb 100644
--- a/Project.toml
+++ b/Project.toml
@@ -2,7 +2,7 @@ name = "IncrementalInference"
 uuid = "904591bb-b899-562f-9e6f-b8df64c7d480"
 keywords = ["MM-iSAMv2", "Bayes tree", "junction tree", "Bayes network", "variable elimination", "graphical models", "SLAM", "inference", "sum-product", "belief-propagation"]
 desc = "Implements the Multimodal-iSAMv2 algorithm."
-version = "0.35.0"
+version = "0.35.1"
 
 [deps]
 ApproxManifoldProducts = "9bbbb610-88a1-53cd-9763-118ce10c1f89"
@@ -91,6 +91,7 @@ RecursiveArrayTools = "2.31.1"
 Reexport = "1"
 SparseDiffTools = "2"
 StaticArrays = "1"
+Statistics = "1"
 StatsBase = "0.32, 0.33, 0.34"
 StructTypes = "1"
 TensorCast = "0.3.3, 0.4"
diff --git a/ext/IncrInfrDiffEqFactorExt.jl b/ext/IncrInfrDiffEqFactorExt.jl
index d9be747d..69d64a84 100644
--- a/ext/IncrInfrDiffEqFactorExt.jl
+++ b/ext/IncrInfrDiffEqFactorExt.jl
@@ -2,6 +2,8 @@ module IncrInfrDiffEqFactorExt
 
 @info "IncrementalInference.jl is loading extensions related to DifferentialEquations.jl"
 
+import Base: show
+
 using DifferentialEquations
 import DifferentialEquations: solve
 
@@ -15,10 +17,30 @@ using DocStringExtensions
 
 export DERelative
 
+import Manifolds: allocate, compose, hat, Identity, vee, log
 
 
 getManifold(de::DERelative{T}) where {T} = getManifold(de.domain)
 
+
+function Base.show(
+  io::IO, 
+  ::Union{<:DERelative{T,O},Type{<:DERelative{T,O}}}
+) where {T,O}
+  println(io, "  DERelative{")
+  println(io, "    ", T)
+  println(io, "    ", O.name.name)
+  println(io, "  }")
+  nothing
+end
+
+Base.show(
+  io::IO, 
+  ::MIME"text/plain", 
+  der::DERelative
+) = show(io, der)
+
+
 """
 $SIGNATURES
 
@@ -28,7 +50,9 @@ DevNotes
 - TODO does not yet incorporate Xi.nanosecond field.
 - TODO does not handle timezone crossing properly yet.
 """
-function _calcTimespan(Xi::AbstractVector{<:DFGVariable})
+function _calcTimespan(
+  Xi::AbstractVector{<:DFGVariable}
+)
   #
   tsmps = getTimestamp.(Xi[1:2]) .|> DateTime .|> datetime2unix
   # toffs = (tsmps .- tsmps[1]) .|> x-> elemType(x.value*1e-3)
@@ -47,10 +71,10 @@ function DERelative(
   f::Function,
   data = () -> ();
   dt::Real = 1,
-  state0::AbstractVector{<:Real} = zeros(getDimension(domain)),
-  state1::AbstractVector{<:Real} = zeros(getDimension(domain)),
+  state0::AbstractVector{<:Real} = allocate(getPointIdentity(domain)), # zeros(getDimension(domain)),
+  state1::AbstractVector{<:Real} = allocate(getPointIdentity(domain)), # zeros(getDimension(domain)),
   tspan::Tuple{<:Real, <:Real} = _calcTimespan(Xi),
-  problemType = DiscreteProblem,
+  problemType = ODEProblem, # DiscreteProblem,
 )
   #
   datatuple = if 2 < length(Xi)
@@ -60,11 +84,11 @@ function DERelative(
     data
   end
   # forward time problem
-  fproblem = problemType(f, state0, tspan, datatuple; dt = dt)
+  fproblem = problemType(f, state0, tspan, datatuple; dt)
   # backward time problem
   bproblem = problemType(f, state1, (tspan[2], tspan[1]), datatuple; dt = -dt)
   # build the IIF recognizable object
-  return DERelative(domain, fproblem, bproblem, datatuple, getSample)
+  return DERelative(domain, fproblem, bproblem, datatuple) #, getSample)
 end
 
 function DERelative(
@@ -75,8 +99,8 @@ function DERelative(
   data = () -> ();
   Xi::AbstractArray{<:DFGVariable} = getVariable.(dfg, labels),
   dt::Real = 1,
-  state0::AbstractVector{<:Real} = zeros(getDimension(domain)),
-  state1::AbstractVector{<:Real} = zeros(getDimension(domain)),
+  state1::AbstractVector{<:Real} = allocate(getPointIdentity(domain)), #zeros(getDimension(domain)),
+  state0::AbstractVector{<:Real} = allocate(getPointIdentity(domain)), #zeros(getDimension(domain)),
   tspan::Tuple{<:Real, <:Real} = _calcTimespan(Xi),
   problemType = DiscreteProblem,
 )
@@ -85,26 +109,32 @@ function DERelative(
     domain,
     f,
     data;
-    dt = dt,
-    state0 = state0,
-    state1 = state1,
-    tspan = tspan,
-    problemType = problemType,
+    dt,
+    state0,
+    state1,
+    tspan,
+    problemType,
   )
 end
 #
 #
 
 # n-ary factor: Xtra splat are variable points (X3::Matrix, X4::Matrix,...)
-function _solveFactorODE!(measArr, prob, u0pts, Xtra...)
+function _solveFactorODE!(
+  measArr, 
+  prob, 
+  u0pts, 
+  Xtra...
+)
   # happens when more variables (n-ary) must be included in DE solve
   for (xid, xtra) in enumerate(Xtra)
     # update the data register before ODE solver calls the function
-    prob.p[xid + 1][:] = xtra[:]
+    prob.p[xid + 1][:] = xtra[:] # FIXME, unlikely to work with ArrayPartition, maybe use MArray and `.=`
   end
 
   # set the initial condition
-  prob.u0[:] = u0pts[:]
+  prob.u0 .= u0pts
+
   sol = DifferentialEquations.solve(prob)
 
   # extract solution from solved ode
@@ -155,21 +185,21 @@ end
 
 
 # NOTE see #1025, CalcFactor should fix `multihypo=` in `cf.__` fields; OBSOLETE
-function (cf::CalcFactor{<:DERelative})(measurement, X...)
+function (cf::CalcFactor{<:DERelative})(
+  measurement, 
+  X...
+)
   #
+  # numerical measurement values
   meas1 = measurement[1]
-  diffOp = measurement[2]
-
+  # work on-manifold via sampleFactor piggy back of particular manifold definition
+  M = measurement[2]
+  # lazy factor pointer
   oderel = cf.factor
-
-  # work on-manifold
-  # diffOp = meas[2]
-  # if backwardSolve else forward
-
   # check direction
-
   solveforIdx = cf.solvefor
-
+  
+  # if backwardSolve else forward
   if solveforIdx > 2
     # need to recalculate new ODE (forward) for change in parameters (solving for 3rd or higher variable)
     solveforIdx = 2
@@ -185,16 +215,10 @@ function (cf::CalcFactor{<:DERelative})(measurement, X...)
   end
 
   # find the difference between measured and predicted.
-  ## assuming the ODE integrated from current X1 through to predicted X2 (ie `meas1[:,idx]`)
-  ## FIXME, obviously this is not going to work for more compilcated groups/manifolds -- must fix this soon!
-  # @show cf._sampleIdx, solveforIdx, meas1
-
-  #FIXME 
-  res = zeros(size(X[2], 1))
-  for i = 1:size(X[2], 1)
-    # diffop( reference?, test? )   <===>   ΔX = test \ reference
-    res[i] = diffOp[i](X[solveforIdx][i], meas1[i])
-  end
+  # assuming the ODE integrated from current X1 through to predicted X2 (ie `meas1[:,idx]`)
+  res_ = compose(M, inv(M, X[solveforIdx]), meas1)
+  res = vee(M, Identity(M), log(M, Identity(M), res_))
+
   return res
 end
 
@@ -249,28 +273,32 @@ function IncrementalInference.sampleFactor(cf::CalcFactor{<:DERelative}, N::Int
   oder = cf.factor
 
   # how many trajectories to propagate?
-  # @show getLabel(cf.fullvariables[2]), getDimension(cf.fullvariables[2])
-  meas = [zeros(getDimension(cf.fullvariables[2])) for _ = 1:N]
+  # 
+  v2T = getVariableType(cf.fullvariables[2])
+  meas = [allocate(getPointIdentity(v2T)) for _ = 1:N]
+  # meas = [zeros(getDimension(cf.fullvariables[2])) for _ = 1:N]
 
   # pick forward or backward direction
   # set boundary condition
-  u0pts = if cf.solvefor == 1
+  u0pts, M = if cf.solvefor == 1
     # backward direction
     prob = oder.backwardProblem
+    M_ = getManifold(getVariableType(cf.fullvariables[1]))
     addOp, diffOp, _, _ = AMP.buildHybridManifoldCallbacks(
-      convert(Tuple, getManifold(getVariableType(cf.fullvariables[1]))),
+      convert(Tuple, M_),
     )
     # getBelief(cf.fullvariables[2]) |> getPoints
-    cf._legacyParams[2]
+    cf._legacyParams[2], M_
   else
     # forward backward
     prob = oder.forwardProblem
+    M_ = getManifold(getVariableType(cf.fullvariables[2]))
     # buffer manifold operations for use during factor evaluation
     addOp, diffOp, _, _ = AMP.buildHybridManifoldCallbacks(
-      convert(Tuple, getManifold(getVariableType(cf.fullvariables[2]))),
+      convert(Tuple, M_),
     )
     # getBelief(cf.fullvariables[1]) |> getPoints
-    cf._legacyParams[1]
+    cf._legacyParams[1], M_
   end
 
   # solve likely elements
@@ -281,17 +309,11 @@ function IncrementalInference.sampleFactor(cf::CalcFactor{<:DERelative}, N::Int
     # _solveFactorODE!(meas, prob, u0pts, i, _maketuplebeyond2args(cf._legacyParams...)...)
   end
 
-  return map(x -> (x, diffOp), meas)
+  # return meas, M
+  return map(x -> (x, M), meas)
 end
 # getDimension(oderel.domain)
 
 
 
-
-
-## the function
-# ode.problem.f.f
-
-#
-
 end # module
\ No newline at end of file
diff --git a/src/ExportAPI.jl b/src/ExportAPI.jl
index 429d2e17..a415dd4d 100644
--- a/src/ExportAPI.jl
+++ b/src/ExportAPI.jl
@@ -1,5 +1,14 @@
 # the IncrementalInference API
 
+
+# reexport
+export ℝ, AbstractManifold
+export Identity, hat , vee, ArrayPartition, exp!, exp, log!, log
+# common groups -- preferred defaults at this time.
+export TranslationGroup, RealCircleGroup
+# common non-groups -- TODO still teething problems to sort out in IIF v0.25-v0.26.
+export Euclidean, Circle
+
 # DFG SpecialDefinitions
 export AbstractDFG,
   getSolverParams,
diff --git a/src/IncrementalInference.jl b/src/IncrementalInference.jl
index 65fff3a0..22243543 100644
--- a/src/IncrementalInference.jl
+++ b/src/IncrementalInference.jl
@@ -19,13 +19,6 @@ using FiniteDifferences
 
 using OrderedCollections: OrderedDict
 
-export ℝ, AbstractManifold
-# export ProductRepr
-# common groups -- preferred defaults at this time.
-export TranslationGroup, RealCircleGroup
-# common non-groups -- TODO still teething problems to sort out in IIF v0.25-v0.26.
-export Euclidean, Circle
-
 import Optim
 
 using Dates,
diff --git a/src/entities/ExtFactors.jl b/src/entities/ExtFactors.jl
index 36dce47e..f6d916e4 100644
--- a/src/entities/ExtFactors.jl
+++ b/src/entities/ExtFactors.jl
@@ -25,5 +25,5 @@ struct DERelative{T <: InferenceVariable, P, D} <: AbstractManifoldMinimize # Ab
   backwardProblem::P
   """ second element of this data tuple is additional variables that will be passed down as a parameter """
   data::D
-  specialSampler::Function
+  # specialSampler::Function
 end
\ No newline at end of file