diff --git a/Project.toml b/Project.toml
index aeb76428a..9cf6ab670 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.74.3"
+version = "1.74.4"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/rulesets/Random/random.jl b/src/rulesets/Random/random.jl
index 9a08f8551..ef9f67b0d 100644
--- a/src/rulesets/Random/random.jl
+++ b/src/rulesets/Random/random.jl
@@ -9,19 +9,23 @@ end
 
 @non_differentiable Broadcast.broadcastable(::AbstractRNG)
 
-@non_differentiable Random.randexp(::AbstractRNG)
-@non_differentiable Random.randstring(::AbstractRNG)
-
-@non_differentiable rand(::AbstractRNG, ::Random.Sampler)
-@non_differentiable rand(::AbstractRNG, ::Integer...)
-@non_differentiable rand(::Type{<:Real})
-@non_differentiable rand(::Type{<:Real}, ::Tuple)
-@non_differentiable rand(::Type{<:Real}, ::Integer...)
-@non_differentiable rand(::Integer...)
-
-@non_differentiable rand!(::AbstractArray)
-@non_differentiable rand!(::AbstractRNG, ::AbstractArray)
-@non_differentiable rand!(::AbstractRNG, ::AbstractArray, ::Type)
+@non_differentiable Random.randstring(::Any...)
+
+# Only samplers whose output does not depend on any differentiable data, or that sample from
+# ranges of Base integer types: e.g. not the ones for sampling from arrays, non-integer ranges,
+# tuples, or user-defined types.
+const NonDifferentiableSampler = Union{
+    Random.SamplerType,
+    Random.SamplerTrivial{<:Random.FloatInterval},
+    Random.SamplerBigFloat,
+    Random.SamplerSimple{<:Union{String,SubString{String},AbstractArray{Char}}},
+    Random.SamplerRangeInt{<:Base.BitInteger},
+    Random.SamplerRangeFast,
+    Random.SamplerRangeNDL{<:Any,<:Base.BitInteger},
+    Random.SamplerBigInt,
+}
+@non_differentiable rand(::AbstractRNG, ::NonDifferentiableSampler)
+@non_differentiable rand!(::AbstractRNG, ::AbstractArray, ::NonDifferentiableSampler)
 
 @non_differentiable randexp(::Any...)
 
diff --git a/test/rulesets/Random/random.jl b/test/rulesets/Random/random.jl
index 6915a3f86..dbff1c824 100644
--- a/test/rulesets/Random/random.jl
+++ b/test/rulesets/Random/random.jl
@@ -32,30 +32,6 @@ Random.rand(d::NormalDistribution) = d.μ + d.σ*randn()
     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}),
-        ]
-        push!(non_differentiables, ((Xoshiro(123),), Float64))
-        push!(non_differentiables, ((Xoshiro(123), 2, 2), Matrix{<:Float64}))
-
-        for (args, xType) in non_differentiables
-            x, dΩ = frule((ZeroTangent(), randn(args...)), rand, args...)
-            @test x isa xType
-            @test dΩ isa NoTangent
-
-            x, pb = rrule(rand, args...)
-            @test x isa xType
-            dself, dargs = Iterators.peel(pb(10.0))
-            @test iszero(dself)
-            @test all(darg isa NoTangent for darg in dargs)
-        end
-
         # Make sure that we do *not* have these set as non_differentiable. as they are differentiable
         @test nothing === frule(
             (ZeroTangent(), Tangent{NormalDistribution}(μ=0.5,σ=2.0)),
@@ -64,4 +40,85 @@ Random.rand(d::NormalDistribution) = d.μ + d.σ*randn()
         )
         @test rrule(rand, NormalDistribution(0.1,1.5)) === nothing
     end
+
+    @testset "randstring" begin
+        for args in (
+            (),
+            (5,),
+            (Xoshiro(123),),
+            (Xoshiro(123), 5),
+            ("ab",),
+            (Xoshiro(123), 'a':'z', 5),
+        )
+            s, ds = frule(
+                (NoTangent(), map(Returns(NoTangent()), args)...), randstring, args...
+            )
+            @test s isa String
+            @test ds isa NoTangent
+            s, pb = rrule(randstring, args...)
+            @test s isa String
+            @test all(darg isa NoTangent for darg in pb(NoTangent()))
+        end
+    end
+
+    @testset "rand(rng, ::Sampler)" begin
+        rng = Xoshiro(123)
+
+        # Samplers without any differentiable data and samplers for integer ranges are non-differentiable
+        for X in (
+            Float64,
+            Float32,
+            Int,
+            Bool,
+            ComplexF64,
+            BigFloat,
+            "abc",
+            SubString("abc", 2),
+            'a':'z',
+            ['a', 'b'],
+            1:4,
+            Base.OneTo(4),
+            Int8(1):Int8(4),
+            UInt128(1):UInt128(4),
+            typemin(Int):typemax(Int),
+            big(1):big(4),
+        )
+            sp = Random.Sampler(rng, X, Val(1))
+            x, dx = frule((NoTangent(), NoTangent(), NoTangent()), rand, rng, sp)
+            @test x isa eltype(sp)
+            @test dx isa NoTangent
+            x, pb = rrule(rand, rng, sp)
+            @test x isa eltype(sp)
+            @test all(darg isa NoTangent for darg in pb(1.0))
+
+            A = Vector{eltype(sp)}(undef, 3)
+            spInf = Random.Sampler(rng, X, Val(Inf))
+            Ω, dΩ = frule(
+                (NoTangent(), NoTangent(), NoTangent(), NoTangent()), rand!, rng, A, spInf
+            )
+            @test Ω === A
+            @test dΩ isa NoTangent
+            Ω, pb! = rrule(rand!, rng, A, spInf)
+            @test Ω === A
+            @test all(darg isa NoTangent for darg in pb!(ones(3)))
+        end
+
+        # Samplers for collections with possibly differentiable elements are not
+        for X in (
+            [1.0, 2.0],
+            (1.0,),
+            (1.0, 2.0),
+            LinRange(0.0, 1.0, 3),
+            0.0:0.5:1.0,
+            UnitRange(1.0, 4.0),
+            Dict(1 => 2.0),
+            Set([1.0]),
+        )
+            @test rrule(rand, rng, Random.Sampler(rng, X, Val(1))) === nothing
+            @test rrule(
+                rand!, rng, Vector{Any}(undef, 3), Random.Sampler(rng, X, Val(Inf))
+            ) === nothing
+        end
+        @test rrule(rand, rng, Random.SamplerRangeNDL(1.5, UInt64(4))) === nothing
+    end
 end