diff --git a/Project.toml b/Project.toml
index 632a6f587..9f4aaf106 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "0.7.17"
+version = "0.7.18"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/rulesets/Random/random.jl b/src/rulesets/Random/random.jl
index 4d03491bf..1afa2466c 100644
--- a/src/rulesets/Random/random.jl
+++ b/src/rulesets/Random/random.jl
@@ -12,11 +12,27 @@ end
 @non_differentiable Random.randexp(::AbstractRNG)
 @non_differentiable Random.randstring(::AbstractRNG)
 
-@non_differentiable rand(::Any)
-@non_differentiable rand(::Any, ::Any)
-@non_differentiable rand(::Any, ::Any, ::Any)
-@non_differentiable rand(::Any, ::Any, ::Any, ::Any)
-@non_differentiable rand(::Any, ::Any, ::Any, ::Any, ::Any)
+@non_differentiable rand()
+@non_differentiable rand(::AbstractRNG)
+@non_differentiable rand(::AbstractRNG, ::Random.Sampler)
+@non_differentiable rand(::AbstractRNG, ::Integer)
+@non_differentiable rand(::AbstractRNG, ::Integer, ::Integer)
+@non_differentiable rand(::AbstractRNG, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::AbstractRNG, ::Integer, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::AbstractRNG, ::Integer, ::Integer, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::Type{<:Real})
+@non_differentiable rand(::Type{<:Real}, ::Tuple)
+@non_differentiable rand(::Type{<:Real}, ::Integer)
+@non_differentiable rand(::Type{<:Real}, ::Integer, ::Integer)
+@non_differentiable rand(::Type{<:Real}, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::Type{<:Real}, ::Integer, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::Type{<:Real}, ::Integer, ::Integer, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::Integer)
+@non_differentiable rand(::Integer, ::Integer)
+@non_differentiable rand(::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::Integer, ::Integer, ::Integer, ::Integer)
+@non_differentiable rand(::Integer, ::Integer, ::Integer, ::Integer, ::Integer)
+
 
 # There are many different 1-3 arg methods, but not varargs
 @non_differentiable rand!(::Any)
diff --git a/test/rulesets/Random/random.jl b/test/rulesets/Random/random.jl
index dec6c4ffe..1f5092450 100644
--- a/test/rulesets/Random/random.jl
+++ b/test/rulesets/Random/random.jl
@@ -1,3 +1,10 @@
+# Simple Distributions like object for testing purposes
+struct NormalDistribution
+    μ
+    σ
+end
+Random.rand(d::NormalDistribution) = d.μ + d.σ*randn()
+
 @testset "random" begin
     @testset "MersenneTwister" begin
         @testset "no args" begin
@@ -19,4 +26,36 @@
             @test all(map(x -> x isa Zero, pb(10)))
         end
     end
+
+    @testset "rand" begin
+        non_differentiables = [
+            ((), Float64),
+            ((MersenneTwister(123),), Float64),
+            ((MersenneTwister(123),2,2), Matrix{<:Float64}),
+            ((Float32,), Float32),
+            ((Float32,2,2), Matrix{<:Float32}),
+            ((Float32,(2,2)), Matrix{<:Float32}),
+            ((2,2), Matrix{<:Float64}),
+        ]
+
+        for (args, xType) in non_differentiables
+            x, dΩ = frule((Zero(), randn(args...)), rand, args...)
+            @test x isa xType
+            @test dΩ isa DoesNotExist
+
+            x, pb = rrule(rand, args...)
+            @test x isa xType
+            dself, dargs = Iterators.peel(pb(10.0))
+            @test dself isa Zero
+            @test all(darg isa DoesNotExist for darg in dargs)
+        end
+
+        # Make sure that we do *not* have these set as non_differentiable. as they are differentiable
+        @test nothing === frule(
+            (Zero(), Composite{NormalDistribution}(μ=0.5,σ=2.0)),
+            rand,
+            NormalDistribution(0.1,1.5),
+        )
+        @test rrule(rand, NormalDistribution(0.1,1.5)) === nothing
+    end
 end