diff --git a/base/compiler/abstractinterpretation.jl b/base/compiler/abstractinterpretation.jl
index faa70830169f0..3c26f2bdef4e5 100644
--- a/base/compiler/abstractinterpretation.jl
+++ b/base/compiler/abstractinterpretation.jl
@@ -876,13 +876,13 @@ end
 
 function abstract_call_method_with_const_args(interp::AbstractInterpreter, result::MethodCallResult,
                                               @nospecialize(f), arginfo::ArgInfo, match::MethodMatch,
-                                              sv::InferenceState)
+                                              sv::InferenceState, invoketypes=nothing)
     if !const_prop_enabled(interp, sv, match)
         return nothing
     end
     res = concrete_eval_call(interp, f, result, arginfo, sv)
     if isa(res, ConstCallResults)
-        add_backedge!(res.const_result.mi, sv)
+        add_backedge!(res.const_result.mi, sv, invoketypes)
         return res
     end
     mi = maybe_get_const_prop_profitable(interp, result, f, arginfo, match, sv)
@@ -1694,7 +1694,7 @@ function abstract_invoke(interp::AbstractInterpreter, (; fargs, argtypes)::ArgIn
     #     argtypes′[i] = t ⊑ a ? t : a
     # end
     const_call_result = abstract_call_method_with_const_args(interp, result,
-        overlayed ? nothing : singleton_type(ft′), arginfo, match, sv)
+        overlayed ? nothing : singleton_type(ft′), arginfo, match, sv, types)
     const_result = nothing
     if const_call_result !== nothing
         if ⊑(typeinf_lattice(interp), const_call_result.rt, rt)
diff --git a/test/precompile.jl b/test/precompile.jl
index 82465d700bb49..47d9a1bb7e860 100644
--- a/test/precompile.jl
+++ b/test/precompile.jl
@@ -892,6 +892,7 @@ precompile_test_harness("invoke") do dir
           """
           module $InvokeModule
               export f, g, h, q, fnc, gnc, hnc, qnc   # nc variants do not infer to a Const
+              export f44320, g44320
               # f is for testing invoke that occurs within a dependency
               f(x::Real) = 0
               f(x::Int) = x < 5 ? 1 : invoke(f, Tuple{Real}, x)
@@ -910,6 +911,11 @@ precompile_test_harness("invoke") do dir
               # q will have some callers invalidated
               q(x::Integer) = 0
               qnc(x::Integer) = rand()-1
+              # Issue #44320
+              f44320(::Int) = 1
+              f44320(::Any) = 2
+              g44320() = invoke(f44320, Tuple{Any}, 0)
+              g44320()
           end
           """)
           write(joinpath(dir, "$CallerModule.jl"),
@@ -934,6 +940,9 @@ precompile_test_harness("invoke") do dir
               internalnc(x::Real) = rand()-1
               internalnc(x::Int) = x < 5 ? rand()+1 : invoke(internalnc, Tuple{Real}, x)
 
+              # Issue #44320
+              f44320(::Real) = 3
+
               # force precompilation
               begin
                   Base.Experimental.@force_compile
@@ -1010,6 +1019,9 @@ precompile_test_harness("invoke") do dir
     m = only(methods(M.callqnci))
     @test m.specializations[1].specTypes == Tuple{typeof(M.callqnci), Int}
 
+    m = only(methods(M.g44320))
+    @test m.specializations[1].cache.max_world == typemax(UInt)
+
     # Precompile specific methods for arbitrary arg types
     invokeme(x) = 1
     invokeme(::Int) = 2