diff --git a/src/rt/diff.jl b/src/rt/diff.jl
index 90a162c0..db07c8b8 100644
--- a/src/rt/diff.jl
+++ b/src/rt/diff.jl
@@ -1,35 +1,24 @@
-import Flow: isconstant, il, dl, cse, prewalk, graphm, syntax
+import Flow: isconstant, il, dl, cse, prewalk, graphm, syntax, @v
 
 vertex(a...) = IVertex{Any}(a...)
 
-∇(f, a::IVertex) =
-  (v(∇₁(f), a),)
+∇graph(f, ∇, a) = (@v(∇ .* ∇₁(f)(a)),)
 
-∇(::typeof(+), a::IVertex, b::IVertex) =
-  v(1), v(1)
+∇graph(::typeof(+), ∇, a, b) = ∇, ∇
 
-∇(::typeof(-), a::IVertex, b::IVertex) =
-  v(1), v(-1)
+∇graph(::typeof(-), ∇, a, b) = ∇, @v(-∇)
 
-∇(::typeof(*), a::IVertex, b::IVertex) =
-  v(transpose, b), v(transpose, a)
+∇graph(::typeof(*), ∇, a, b) = map(x->@v(∇ * transpose(x)), (b, a))
 
-function ∇v(v::IVertex, chain::Vector{IVertex}, out = d())
+function ∇graph(v::IVertex, ∇, out = d())
   if isconstant(v)
     @assert !haskey(out, value(v))
-    out[value(v)] = length(chain) == 1 ?
-      first(chain) :
-      foldl((x, y) -> vertex(*, x, y), chain)
+    out[value(v)] = ∇
   else
-    ∇s = ∇(value(v), inputs(v)...)
-    for (v′, ∇′) in zip(inputs(v), ∇s)
-      ∇v(v′, (value(∇′) ≠ 1 ? push!(copy(chain), ∇′) : chain), out)
+    ∇′s = ∇graph(value(v), ∇, inputs(v)...)
+    for (v′, ∇′) in zip(inputs(v), ∇′s)
+      ∇graph(v′, ∇′, out)
     end
   end
   return out
 end
-
-∇v(v::Vertex, chain::Vector) = ∇v(convert(IVertex, v), convert(Vector{IVertex}, chain))
-
-∇v(v::Vertex, ∂::Vertex) = ∇v(v, [∂])
-