diff --git a/src/Flux.jl b/src/Flux.jl
index f56e5350..641a1af3 100644
--- a/src/Flux.jl
+++ b/src/Flux.jl
@@ -13,11 +13,13 @@ abstract Activation <: Model
 back!(m::Model, ∇) = error("Backprop not implemented for $(typeof(m))")
 update!(m::Model, η) = m
 
-include("utils.jl")
+include("rt/diff.jl")
+
 include("cost.jl")
 include("activation.jl")
 include("layers/input.jl")
 include("layers/dense.jl")
 include("layers/sequence.jl")
+include("utils.jl")
 
 end # module
diff --git a/src/activation.jl b/src/activation.jl
index f0c0a82d..a9832c7e 100644
--- a/src/activation.jl
+++ b/src/activation.jl
@@ -3,6 +3,8 @@ export Sigmoid
 σ(x) = 1/(1+exp(-x))
 σ′(x) = σ(x)*(1-σ(x))
 
+∇₁(::typeof(σ)) = σ′
+
 type Sigmoid <: Activation
   in::Vector{Float32}
   out::Vector{Float32}
diff --git a/src/rt/diff.jl b/src/rt/diff.jl
new file mode 100644
index 00000000..90a162c0
--- /dev/null
+++ b/src/rt/diff.jl
@@ -0,0 +1,35 @@
+import Flow: isconstant, il, dl, cse, prewalk, graphm, syntax
+
+vertex(a...) = IVertex{Any}(a...)
+
+∇(f, a::IVertex) =
+  (v(∇₁(f), a),)
+
+∇(::typeof(+), a::IVertex, b::IVertex) =
+  v(1), v(1)
+
+∇(::typeof(-), a::IVertex, b::IVertex) =
+  v(1), v(-1)
+
+∇(::typeof(*), a::IVertex, b::IVertex) =
+  v(transpose, b), v(transpose, a)
+
+function ∇v(v::IVertex, chain::Vector{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)
+  else
+    ∇s = ∇(value(v), inputs(v)...)
+    for (v′, ∇′) in zip(inputs(v), ∇s)
+      ∇v(v′, (value(∇′) ≠ 1 ? push!(copy(chain), ∇′) : chain), 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, [∂])
+