diff --git a/src/bijectors/leaky_relu.jl b/src/bijectors/leaky_relu.jl
new file mode 100644
index 00000000..ffca00c7
--- /dev/null
+++ b/src/bijectors/leaky_relu.jl
@@ -0,0 +1,93 @@
+"""
+    LeakyReLU{T, N}(α::T) <: Bijector{N}
+
+Defines the invertible mapping
+
+    x ↦ x if x ≥ 0 else αx
+
+where α > 0.
+"""
+struct LeakyReLU{T, N} <: Bijector{N}
+    α::T
+end
+
+LeakyReLU(α::T; dim::Val{N} = Val(0)) where {T<:Real, N} = LeakyReLU{T, N}(α)
+LeakyReLU(α::T; dim::Val{N} = Val(D)) where {D, T<:AbstractArray{<:Real, D}, N} = LeakyReLU{T, N}(α)
+
+up1(b::LeakyReLU{T, N}) where {T, N} = LeakyReLU{T, N + 1}(b.α)
+
+# (N=0) Univariate case
+function (b::LeakyReLU{<:Any, 0})(x::Real)
+    mask = x < zero(x)
+    return mask * b.α * x + !mask * x
+end
+(b::LeakyReLU{<:Any, 0})(x::AbstractVector{<:Real}) = map(b, x)
+
+function Base.inv(b::LeakyReLU{<:Any,N}) where N
+    invα = inv.(b.α)
+    return LeakyReLU{typeof(invα),N}(invα)
+end
+
+function logabsdetjac(b::LeakyReLU{<:Any, 0}, x::Real)
+    mask = x < zero(x)
+    J = mask * b.α + (1 - mask) * one(x)
+    return log(abs(J))
+end
+logabsdetjac(b::LeakyReLU{<:Real, 0}, x::AbstractVector{<:Real}) = map(x -> logabsdetjac(b, x), x)
+
+
+# We implement `forward` by hand since we can re-use the computation of
+# the Jacobian of the transformation. This will lead to faster sampling
+# when using `rand` on a `TransformedDistribution` making use of `LeakyReLU`.
+function forward(b::LeakyReLU{<:Any, 0}, x::Real)
+    mask = x < zero(x)
+    J = mask * b.α + !mask * one(x)
+    return (rv=J * x, logabsdetjac=log(abs(J)))
+end
+
+# Batched version
+function forward(b::LeakyReLU{<:Any, 0}, x::AbstractVector)
+    J = let T = eltype(x), z = zero(T), o = one(T)
+        @. (x < z) * b.α + (x > z) * o
+    end
+    return (rv=J .* x, logabsdetjac=log.(abs.(J)))
+end
+
+# (N=1) Multivariate case
+function (b::LeakyReLU{<:Any, 1})(x::AbstractVecOrMat)
+    return let z = zero(eltype(x))
+        @. (x < z) * b.α * x + (x > z) * x
+    end
+end
+
+function logabsdetjac(b::LeakyReLU{<:Any, 1}, x::AbstractVecOrMat)
+    # Is really diagonal of jacobian
+    J = let T = eltype(x), z = zero(T), o = one(T)
+        @. (x < z) * b.α + (x > z) * o
+    end
+
+    if x isa AbstractVector
+        return sum(log.(abs.(J)))
+    elseif x isa AbstractMatrix
+        return vec(sum(log.(abs.(J)); dims = 1))  # sum along column
+    end
+end
+
+# We implement `forward` by hand since we can re-use the computation of
+# the Jacobian of the transformation. This will lead to faster sampling
+# when using `rand` on a `TransformedDistribution` making use of `LeakyReLU`.
+function forward(b::LeakyReLU{<:Any, 1}, x::AbstractVecOrMat)
+    # Is really diagonal of jacobian
+    J = let T = eltype(x), z = zero(T), o = one(T)
+        @. (x < z) * b.α + (x > z) * o
+    end
+
+    if x isa AbstractVector
+        logjac = sum(log.(abs.(J)))
+    elseif x isa AbstractMatrix
+        logjac = vec(sum(log.(abs.(J)); dims = 1))  # sum along column
+    end
+
+    y = J .* x
+    return (rv=y, logabsdetjac=logjac)
+end
diff --git a/src/interface.jl b/src/interface.jl
index a1a8d462..cde2bcfb 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -155,6 +155,7 @@ include("bijectors/truncated.jl")
 # Normalizing flow related
 include("bijectors/planar_layer.jl")
 include("bijectors/radial_layer.jl")
+include("bijectors/leaky_relu.jl")
 include("bijectors/coupling.jl")
 include("bijectors/normalise.jl")
 
diff --git a/test/bijectors/leaky_relu.jl b/test/bijectors/leaky_relu.jl
new file mode 100644
index 00000000..63ba8c18
--- /dev/null
+++ b/test/bijectors/leaky_relu.jl
@@ -0,0 +1,86 @@
+using Test
+
+using Bijectors
+using Bijectors: LeakyReLU
+
+using LinearAlgebra
+using ForwardDiff
+
+true_logabsdetjac(b::Bijector{0}, x::Real) = (log ∘ abs)(ForwardDiff.derivative(b, x))
+true_logabsdetjac(b::Bijector{0}, x::AbstractVector) = (log ∘ abs).(ForwardDiff.derivative.(b, x))
+true_logabsdetjac(b::Bijector{1}, x::AbstractVector) = logabsdet(ForwardDiff.jacobian(b, x))[1]
+true_logabsdetjac(b::Bijector{1}, xs::AbstractMatrix) = mapreduce(z -> true_logabsdetjac(b, z), vcat, eachcol(xs))
+
+@testset "0-dim parameter, 0-dim input" begin
+    b = LeakyReLU(0.1; dim=Val(0))
+    x = 1.
+    @test inv(b)(b(x)) == x
+    @test inv(b)(b(-x)) == -x
+
+    # Mixing of types
+    # 1. Changes in input-type
+    @assert eltype(b(Float32(1.))) == Float64
+    @assert eltype(b(Float64(1.))) == Float64
+
+    # 2. Changes in parameter-type
+    b = LeakyReLU(Float32(0.1); dim=Val(0))
+    @assert eltype(b(Float32(1.))) == Float32
+    @assert eltype(b(Float64(1.))) == Float64
+
+    # logabsdetjac
+    @test logabsdetjac(b, x) == true_logabsdetjac(b, x)
+    @test logabsdetjac(b, Float32(x)) == true_logabsdetjac(b, x)
+
+    # Batch
+    xs = randn(10)
+    @test logabsdetjac(b, xs) == true_logabsdetjac(b, xs)
+    @test logabsdetjac(b, Float32.(x)) == true_logabsdetjac(b, Float32.(x))
+
+    @test logabsdetjac(b, -xs) == true_logabsdetjac(b, -xs)
+    @test logabsdetjac(b, -Float32.(xs)) == true_logabsdetjac(b, -Float32.(xs))
+
+    # Forward
+    f = forward(b, xs)
+    @test f.logabsdetjac ≈ logabsdetjac(b, xs)
+    @test f.rv ≈ b(xs)
+
+    f = forward(b, Float32.(xs))
+    @test f.logabsdetjac == logabsdetjac(b, Float32.(xs))
+    @test f.rv ≈ b(Float32.(xs))
+end
+
+@testset "0-dim parameter, 1-dim input" begin
+    d = 2
+
+    b = LeakyReLU(0.1; dim=Val(1))
+    x = ones(d)
+    @test inv(b)(b(x)) == x
+    @test inv(b)(b(-x)) == -x
+
+    # Batch
+    xs = randn(d, 10)
+    @test logabsdetjac(b, xs) == true_logabsdetjac(b, xs)
+    @test logabsdetjac(b, Float32.(x)) == true_logabsdetjac(b, Float32.(x))
+
+    @test logabsdetjac(b, -xs) == true_logabsdetjac(b, -xs)
+    @test logabsdetjac(b, -Float32.(xs)) == true_logabsdetjac(b, -Float32.(xs))
+
+    # Forward
+    f = forward(b, xs)
+    @test f.logabsdetjac ≈ logabsdetjac(b, xs)
+    @test f.rv ≈ b(xs)
+
+    f = forward(b, Float32.(xs))
+    @test f.logabsdetjac == logabsdetjac(b, Float32.(xs))
+    @test f.rv ≈ b(Float32.(xs))
+
+    # Mixing of types
+    # 1. Changes in input-type
+    @assert eltype(b(ones(Float32, 2))) == Float64
+    @assert eltype(b(ones(Float64, 2))) == Float64
+
+    # 2. Changes in parameter-type
+    b = LeakyReLU(Float32(0.1); dim=Val(1))
+    @assert eltype(b(ones(Float32, 2))) == Float32
+    @assert eltype(b(ones(Float64, 2))) == Float64
+end
diff --git a/test/interface.jl b/test/interface.jl
index 1fa6d0fe..cae79ee8 100644
--- a/test/interface.jl
+++ b/test/interface.jl
@@ -7,7 +7,7 @@ using Tracker
 using DistributionsAD
 
 using Bijectors
-using Bijectors: Log, Exp, Shift, Scale, Logit, SimplexBijector, PDBijector, Permute, PlanarLayer, RadialLayer, Stacked, TruncatedBijector, ADBijector
+using Bijectors: Log, Exp, Shift, Scale, Logit, SimplexBijector, PDBijector, Permute, PlanarLayer, RadialLayer, Stacked, TruncatedBijector, ADBijector, LeakyReLU
 
 Random.seed!(123)
 
@@ -159,7 +159,10 @@ end
         (SimplexBijector(), mapslices(z -> normalize(z, 1), rand(2, 3); dims = 1)),
         (stack(Exp{0}(), Scale(2.0)), randn(2, 3)),
         (Stacked((Exp{1}(), SimplexBijector()), [1:1, 2:3]),
-         mapslices(z -> normalize(z, 1), rand(3, 2); dims = 1))
+         mapslices(z -> normalize(z, 1), rand(3, 2); dims = 1)),
+        (LeakyReLU(0.1), randn(3)),
+        (LeakyReLU(Float32(0.1)), randn(3)),
+        (LeakyReLU(0.1; dim = Val(1)), randn(2, 3))
     ]
 
     for (b, xs) in bs_xs
@@ -172,7 +175,6 @@ end
             x = D == 0 ? xs[1] : xs[:, 1]
 
             y = @inferred b(x)
-
             ys = @inferred b(xs)
 
             # Computations which do not have closed-form implementations are not necessarily
diff --git a/test/runtests.jl b/test/runtests.jl
index 3d6acba9..5f05f71c 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -28,9 +28,11 @@ if GROUP == "All" || GROUP == "Interface"
     include("transform.jl")
     include("norm_flows.jl")
     include("bijectors/permute.jl")
+    include("bijectors/leaky_relu.jl")
     include("bijectors/coupling.jl")
 end
 
 if !is_TRAVIS && (GROUP == "All" || GROUP == "AD")
     include("ad/distributions.jl")
 end
+