diff --git a/src/extensions/Distributions.jl b/src/extensions/Distributions.jl
new file mode 100644
index 0000000..6a3cfbf
--- /dev/null
+++ b/src/extensions/Distributions.jl
@@ -0,0 +1,13 @@
+export normlogpdf
+
+# watch https://github.com/JuliaStats/Distributions.jl/issues/1183
+
+"""
+GPU automatic differentiable version for the logpdf function of normal distributions.
+Adding an epsilon value to guarantee numeric stability if sigma is exactly zero
+(e.g. if relu is used in output layer).
+"""
+function normlogpdf(μ, σ, x; ϵ = 1.0f-8)
+    z = (x .- μ) ./ (σ .+ ϵ)
+    -(z .^ 2 .+ log(2.0f0π)) / 2.0f0 .- log.(σ .+ ϵ)
+end
diff --git a/src/extensions/extensions.jl b/src/extensions/extensions.jl
index 9375b69..f4a17d9 100644
--- a/src/extensions/extensions.jl
+++ b/src/extensions/extensions.jl
@@ -3,3 +3,4 @@ include("CUDA.jl")
 include("Zygote.jl")
 include("ReinforcementLearningBase.jl")
 include("ElasticArrays.jl")
+include("Distributions.jl")
diff --git a/test/extensions.jl b/test/extensions.jl
index 07659dc..6a3265a 100644
--- a/test/extensions.jl
+++ b/test/extensions.jl
@@ -14,3 +14,23 @@
     clip_by_global_norm!(gs, ps, 4.0f0)
     @test isapprox(gs[:x], [0.0 0.0 0.0; 0.0 0.0 0.0])
 end
+
+
+@testset "Distributions" begin
+    @test isapprox(logpdf(Normal(), 2), normlogpdf(0, 1, 2))
+    @test isapprox(logpdf.([Normal(), Normal()], [2, 10]), normlogpdf([0, 0], [1, 1], [2, 10]))
+
+    # Test numeric stability for 0 sigma
+    @test isnan(normlogpdf(0, 0, 2, ϵ=0))
+    @test !isnan(normlogpdf(0, 0, 2))
+
+    if CUDA.functional()
+        cpu_grad = Zygote.gradient([0.2, 0.5]) do x
+            sum(logpdf.([Normal(1,0.1), Normal(2,0.2)], x))
+        end
+        gpu_grad = Zygote.gradient(cu([0.2, 0.5])) do x
+            sum(normlogpdf(cu([1, 2]), cu([0.1, 0.2]),x))
+        end
+        @test isapprox(cpu_grad[1], gpu_grad[1] |> Array)
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index b71ad52..a563f68 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,7 +3,7 @@ using ReinforcementLearningCore
 using Random
 using Test
 using StatsBase
-using Distributions: probs
+using Distributions: probs, Normal, logpdf
 using ReinforcementLearningEnvironments
 using Flux
 using Zygote