diff --git a/src/rulesets/Base/arraymath.jl b/src/rulesets/Base/arraymath.jl
index 078bb602a..765b55b48 100644
--- a/src/rulesets/Base/arraymath.jl
+++ b/src/rulesets/Base/arraymath.jl
@@ -434,6 +434,21 @@ function rrule(::typeof(-), x::AbstractArray)
     return -x, negation_pullback
 end
 
+#####
+##### Subtraction
+#####
+
+frule((_, Δx, Δy), ::typeof(-), x::AbstractArray, y::AbstractArray) = x - y, Δx - Δy
+
+function rrule(::typeof(-), x::AbstractArray, y::AbstractArray)
+    xproj = ProjectTo(x)
+    yproj = ProjectTo(y)
+    function subtract_pullback(dy_raw)
+        dy = unthunk(dy_raw)  # projs will otherwise unthunk twice
+        return (NoTangent(), xproj(dy), yproj(-dy))
+    end
+    return x - y, subtract_pullback
+end
 
 #####
 ##### Addition (Multiarg `+`)
diff --git a/test/rulesets/Base/arraymath.jl b/test/rulesets/Base/arraymath.jl
index 2682f3b8a..2099b9b3b 100644
--- a/test/rulesets/Base/arraymath.jl
+++ b/test/rulesets/Base/arraymath.jl
@@ -217,4 +217,13 @@
         @gpu test_rrule(+, randn(4, 4), randn(4, 4), randn(4, 4))
         @gpu test_rrule(+, randn(3), randn(3,1), randn(3,1,1))
     end
+
+    @testset "subtraction" begin
+        # fwd
+        @gpu test_frule(-, randn(2), randn(2))
+        # rev
+        @gpu test_rrule(-, randn(4, 4), randn(4, 4))
+        @gpu test_rrule(-, randn(4), randn(ComplexF64, 4))
+        @gpu test_rrule(-, randn(3), randn(3, 1))
+    end
 end