diff --git a/Project.toml b/Project.toml
index 35e03e2924..8a7cd147b4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -95,7 +95,7 @@ DataInterpolations = "6.4"
 DataStructures = "0.17, 0.18"
 DeepDiffs = "1"
 DelayDiffEq = "5.50"
-DiffEqBase = "6.165.1"
+DiffEqBase = "6.170.1"
 DiffEqCallbacks = "2.16, 3, 4"
 DiffEqNoiseProcess = "5"
 DiffRules = "0.1, 1.0"
diff --git a/src/systems/nonlinear/initializesystem.jl b/src/systems/nonlinear/initializesystem.jl
index 50c0862863..5995272be9 100644
--- a/src/systems/nonlinear/initializesystem.jl
+++ b/src/systems/nonlinear/initializesystem.jl
@@ -589,26 +589,41 @@ function SciMLBase.remake_initialization_data(
     return SciMLBase.remake_initialization_data(sys, kws, newu0, t0, newp, newu0, newp)
 end
 
+function promote_u0_p(u0, p::MTKParameters, t0)
+    u0 = DiffEqBase.promote_u0(u0, p.tunable, t0)
+    u0 = DiffEqBase.promote_u0(u0, p.initials, t0)
+
+    tunables = DiffEqBase.promote_u0(p.tunable, u0, t0)
+    initials = DiffEqBase.promote_u0(p.initials, u0, t0)
+    p = SciMLStructures.replace(SciMLStructures.Tunable(), p, tunables)
+    p = SciMLStructures.replace(SciMLStructures.Initials(), p, initials)
+
+    return u0, p
+end
+
+function promote_u0_p(u0, p::AbstractArray, t0)
+    return DiffEqBase.promote_u0(u0, p, t0), DiffEqBase.promote_u0(p, u0, t0)
+end
+
 function SciMLBase.late_binding_update_u0_p(
         prob, sys::AbstractSystem, u0, p, t0, newu0, newp)
     supports_initialization(sys) || return newu0, newp
-    u0 === missing && return newu0, (p === missing ? copy(newp) : newp)
+
+    initdata = prob.f.initialization_data
+    meta = initdata === nothing ? nothing : initdata.metadata
+
+    newu0, newp = promote_u0_p(newu0, newp, t0)
+
     # non-symbolic u0 updates initials...
     if !(eltype(u0) <: Pair)
         # if `p` is not provided or is symbolic
         p === missing || eltype(p) <: Pair || return newu0, newp
         (newu0 === nothing || isempty(newu0)) && return newu0, newp
-        initdata = prob.f.initialization_data
         initdata === nothing && return newu0, newp
         meta = initdata.metadata
         meta isa InitializationMetadata || return newu0, newp
         newp = p === missing ? copy(newp) : newp
-        initials, repack, alias = SciMLStructures.canonicalize(
-            SciMLStructures.Initials(), newp)
-        if eltype(initials) != eltype(newu0)
-            initials = DiffEqBase.promote_u0(initials, newu0, t0)
-            newp = repack(initials)
-        end
+
         if length(newu0) != length(prob.u0)
             throw(ArgumentError("Expected `newu0` to be of same length as unknowns ($(length(prob.u0))). Got $(typeof(newu0)) of length $(length(newu0))"))
         end
@@ -617,17 +632,6 @@ function SciMLBase.late_binding_update_u0_p(
     end
 
     newp = p === missing ? copy(newp) : newp
-    newu0 = DiffEqBase.promote_u0(newu0, newp, t0)
-    tunables, repack, alias = SciMLStructures.canonicalize(SciMLStructures.Tunable(), newp)
-    if eltype(tunables) != eltype(newu0)
-        tunables = DiffEqBase.promote_u0(tunables, newu0, t0)
-        newp = repack(tunables)
-    end
-    initials, repack, alias = SciMLStructures.canonicalize(SciMLStructures.Initials(), newp)
-    if eltype(initials) != eltype(newu0)
-        initials = DiffEqBase.promote_u0(initials, newu0, t0)
-        newp = repack(initials)
-    end
 
     allsyms = all_symbols(sys)
     for (k, v) in u0
@@ -646,6 +650,37 @@ function SciMLBase.late_binding_update_u0_p(
     return newu0, newp
 end
 
+function DiffEqBase.get_updated_symbolic_problem(sys::AbstractSystem, prob; kw...)
+    supports_initialization(sys) || return prob
+    initdata = prob.f.initialization_data
+    initdata isa SciMLBase.OverrideInitData || return prob
+    meta = initdata.metadata
+    meta isa InitializationMetadata || return prob
+    meta.get_updated_u0 === nothing && return prob
+
+    u0 = state_values(prob)
+    u0 === nothing && return prob
+
+    p = parameter_values(prob)
+    t0 = is_time_dependent(prob) ? current_time(prob) : nothing
+
+    if p isa MTKParameters
+        buffer = p.initials
+    else
+        buffer = p
+    end
+
+    u0 = DiffEqBase.promote_u0(u0, buffer, t0)
+
+    if ArrayInterface.ismutable(u0)
+        T = typeof(u0)
+    else
+        T = StaticArrays.similar_type(u0)
+    end
+
+    return remake(prob; u0 = T(meta.get_updated_u0(prob, initdata.initializeprob)))
+end
+
 """
     $(TYPEDSIGNATURES)
 
diff --git a/src/systems/problem_utils.jl b/src/systems/problem_utils.jl
index 41c64b78c5..47bf3c678d 100644
--- a/src/systems/problem_utils.jl
+++ b/src/systems/problem_utils.jl
@@ -769,7 +769,7 @@ properly.
 
 $(TYPEDFIELDS)
 """
-struct InitializationMetadata{R <: ReconstructInitializeprob, SIU}
+struct InitializationMetadata{R <: ReconstructInitializeprob, GUU, SIU}
     """
     The `u0map` used to construct the initialization.
     """
@@ -796,12 +796,62 @@ struct InitializationMetadata{R <: ReconstructInitializeprob, SIU}
     """
     oop_reconstruct_u0_p::R
     """
+    A function which takes `(prob, initializeprob)` and return the `u0` to use for the problem.
+    """
+    get_updated_u0::GUU
+    """
     A function which takes the `u0` of the problem and sets
     `Initial.(unknowns(sys))`.
     """
     set_initial_unknowns!::SIU
 end
 
+"""
+    $(TYPEDEF)
+
+A callable struct to use as the `get_updated_u0` field of `InitializationMetadata`.
+Returns the value to use for the `u0` of the problem. 
+
+# Fields
+
+$(TYPEDFIELDS)
+"""
+struct GetUpdatedU0{GG, GIU}
+    """
+    Mask with length `length(unknowns(sys))` denoting indices of variables which should
+    take the guess value from `initializeprob`.
+    """
+    guessvars::BitVector
+    """
+    Function which returns the values of variables in `initializeprob` for which
+    `guessvars` is `true`, in the order they occur in `unknowns(sys)`.
+    """
+    get_guessvars::GG
+    """
+    Function which returns `Initial.(unknowns(sys))` as a `Vector`.
+    """
+    get_initial_unknowns::GIU
+end
+
+function GetUpdatedU0(sys::AbstractSystem, initsys::AbstractSystem, op::AbstractDict)
+    dvs = unknowns(sys)
+    eqs = equations(sys)
+    guessvars = trues(length(dvs))
+    for (i, var) in enumerate(dvs)
+        guessvars[i] = !isequal(get(op, var, nothing), Initial(var))
+    end
+    get_guessvars = getu(initsys, dvs[guessvars])
+    get_initial_unknowns = getu(sys, Initial.(dvs))
+    return GetUpdatedU0(guessvars, get_guessvars, get_initial_unknowns)
+end
+
+function (guu::GetUpdatedU0)(prob, initprob)
+    buffer = guu.get_initial_unknowns(prob)
+    algebuf = view(buffer, guu.guessvars)
+    copyto!(algebuf, guu.get_guessvars(initprob))
+    return buffer
+end
+
 """
     $(TYPEDSIGNATURES)
 
@@ -840,10 +890,15 @@ function maybe_build_initialization_problem(
     end
     initializeprob = remake(initializeprob; p = initp)
 
+    get_initial_unknowns = if is_time_dependent(sys)
+        GetUpdatedU0(sys, initializeprob.f.sys, op)
+    else
+        nothing
+    end
     meta = InitializationMetadata(
         u0map, pmap, guesses, Vector{Equation}(initialization_eqs),
         use_scc, ReconstructInitializeprob(sys, initializeprob.f.sys),
-        setp(sys, Initial.(unknowns(sys))))
+        get_initial_unknowns, setp(sys, Initial.(unknowns(sys))))
 
     if is_time_dependent(sys)
         all_init_syms = Set(all_symbols(initializeprob))
diff --git a/test/initializationsystem.jl b/test/initializationsystem.jl
index 2804c70833..5c36fcba3e 100644
--- a/test/initializationsystem.jl
+++ b/test/initializationsystem.jl
@@ -1512,3 +1512,54 @@ end
     @inferred remake(prob; u0 = 2 .* prob.u0, p = prob.p)
     @inferred solve(prob)
 end
+
+@testset "Issue#3570, #3552: `Initial`s/guesses are copied to `u0` during `solve`/`init`" begin
+    @parameters g
+    @variables x(t) [state_priority = 10] y(t) λ(t)
+    eqs = [D(D(x)) ~ λ * x
+           D(D(y)) ~ λ * y - g
+           x^2 + y^2 ~ 1]
+    @mtkbuild pend = ODESystem(eqs, t)
+
+    prob = ODEProblem(
+        pend, [x => (√2 / 2), D(x) => 0.0], (0.0, 1.5),
+        [g => 1], guesses = [λ => 1, y => √2 / 2])
+    sol = solve(prob)
+
+    @testset "Guesses of initialization problem copied to algebraic variables" begin
+        prob.f.initialization_data.initializeprob[λ] = 1.0
+        prob2 = DiffEqBase.get_updated_symbolic_problem(
+            pend, prob; u0 = prob.u0, p = prob.p)
+        @test prob2[λ] ≈ 1.0
+    end
+
+    @testset "Initial values for algebraic variables are retained" begin
+        prob2 = ODEProblem(
+            pend, [x => (√2 / 2), D(y) => 0.0], (0.0, 1.5),
+            [g => 1], guesses = [λ => 1, y => √2 / 2])
+        sol = solve(prob)
+        @test SciMLBase.successful_retcode(sol)
+        prob3 = DiffEqBase.get_updated_symbolic_problem(
+            pend, prob2; u0 = prob2.u0, p = prob2.p)
+        @test prob3[D(y)] ≈ 0.0
+    end
+
+    @testset "`setsym_oop`" begin
+        setter = setsym_oop(prob, [Initial(x)])
+        (u0, p) = setter(prob, [0.8])
+        new_prob = remake(prob; u0, p, initializealg = BrownFullBasicInit())
+        new_sol = solve(new_prob)
+        @test new_sol[x, 1] ≈ 0.8
+        integ = init(new_prob)
+        @test integ[x] ≈ 0.8
+    end
+
+    @testset "`setsym`" begin
+        @test prob.ps[Initial(x)] ≈ √2 / 2
+        prob.ps[Initial(x)] = 0.8
+        sol = solve(prob; initializealg = BrownFullBasicInit())
+        @test sol[x, 1] ≈ 0.8
+        integ = init(prob; initializealg = BrownFullBasicInit())
+        @test integ[x] ≈ 0.8
+    end
+end