diff --git a/Project.toml b/Project.toml
index 1815b08..43205ed 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "DistributionsAD"
 uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
-version = "0.6.35"
+version = "0.6.36"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
@@ -27,8 +27,8 @@ ChainRules = "1"
 ChainRulesCore = "1"
 Compat = "3.6"
 DiffRules = "0.1, 1.0"
-Distributions = "0.25.32"
-FillArrays = "0.8, 0.9, 0.10, 0.11, 0.12"
+Distributions = "0.25.41"
+FillArrays = "0.9, 0.10, 0.11, 0.12"
 NaNMath = "0.3"
 PDMats = "0.9, 0.10, 0.11"
 Requires = "1"
diff --git a/src/DistributionsAD.jl b/src/DistributionsAD.jl
index 92349bf..9be245a 100644
--- a/src/DistributionsAD.jl
+++ b/src/DistributionsAD.jl
@@ -1,9 +1,9 @@
 module DistributionsAD
 
-using PDMats, 
-      LinearAlgebra, 
-      Distributions, 
-      Random, 
+using PDMats,
+      LinearAlgebra,
+      Distributions,
+      Random,
       SpecialFunctions,
       StatsFuns,
       Compat,
@@ -16,20 +16,20 @@ using PDMats,
 
 using SpecialFunctions: logabsgamma, digamma
 using LinearAlgebra: copytri!, AbstractTriangular
-using Distributions: AbstractMvLogNormal, 
+using Distributions: AbstractMvLogNormal,
                      ContinuousMultivariateDistribution
 using Base.Iterators: drop
 
 import StatsBase
-import StatsFuns: logsumexp, 
-                  binomlogpdf, 
-                  nbinomlogpdf, 
-                  poislogpdf, 
+import StatsFuns: logsumexp,
+                  binomlogpdf,
+                  nbinomlogpdf,
+                  poislogpdf,
                   nbetalogpdf
-import Distributions: MvNormal, 
-                      MvLogNormal, 
-                      logpdf, 
-                      quantile, 
+import Distributions: MvNormal,
+                      MvLogNormal,
+                      logpdf,
+                      quantile,
                       PoissonBinomial,
                       Binomial,
                       BetaBinomial,
@@ -53,7 +53,6 @@ include("multivariate.jl")
 include("matrixvariate.jl")
 include("flatten.jl")
 
-include("chainrules.jl")
 include("zygote.jl")
 
 @init begin
diff --git a/src/chainrules.jl b/src/chainrules.jl
deleted file mode 100644
index 45c8ee7..0000000
--- a/src/chainrules.jl
+++ /dev/null
@@ -1,11 +0,0 @@
-## Uniform ##
-
-@scalar_rule(
-    uniformlogpdf(a, b, x),
-    @setup(
-        insupport = a <= x <= b,
-        diff = b - a,
-        c = insupport ? inv(diff) : inv(one(diff)),
-    ),
-    (c, -c, ZeroTangent()),
-)
diff --git a/src/flatten.jl b/src/flatten.jl
index f386a4b..d175049 100644
--- a/src/flatten.jl
+++ b/src/flatten.jl
@@ -8,8 +8,8 @@ function getexpr(Tdist)
     x = gensym()
     fnames = fieldnames(Tdist)
     flattened_args = Expr(:tuple, [:(dist.$f) for f in fnames]...)
-    func = Expr(:->, 
-                Expr(:tuple, fnames..., x), 
+    func = Expr(:->,
+                Expr(:tuple, fnames..., x),
                 Expr(:block,
                     Expr(:call, :logpdf,
                         Expr(:call, :($Tdist), fnames...),
@@ -58,7 +58,6 @@ const flattened_dists = [   Bernoulli,
                             TDist,
                             TriangularDist,
                             Triweight,
-                            TuringUniform,
                         ]
 for T in flattened_dists
     @eval toflatten(::$T) = true
diff --git a/src/tracker.jl b/src/tracker.jl
index e0fe1e2..414d442 100644
--- a/src/tracker.jl
+++ b/src/tracker.jl
@@ -208,36 +208,33 @@ adapt_randn(rng::AbstractRNG, x::TrackedArray, dims...) = adapt_randn(rng, data(
 
 ## Uniform ##
 
-Distributions.Uniform(a::TrackedReal, b::Real) = TuringUniform{TrackedReal}(a, b)
-Distributions.Uniform(a::Real, b::TrackedReal) = TuringUniform{TrackedReal}(a, b)
-Distributions.Uniform(a::TrackedReal, b::TrackedReal) = TuringUniform{TrackedReal}(a, b)
-Distributions.logpdf(d::Uniform, x::TrackedReal) = uniformlogpdf(d.a, d.b, x)
-
-uniformlogpdf(a::Real, b::Real, x::TrackedReal) = track(uniformlogpdf, a, b, x)
-uniformlogpdf(a::TrackedReal, b::TrackedReal, x::Real) = track(uniformlogpdf, a, b, x)
-uniformlogpdf(a::TrackedReal, b::TrackedReal, x::TrackedReal) = track(uniformlogpdf, a, b, x)
-@grad function uniformlogpdf(a, b, x)
-    # compute log pdf
-    diff = data(b) - data(a)
-    insupport = a <= data(x) <= b
-    lp = insupport ? -log(diff) : log(zero(diff))
-
-    function pullback(Δ)
-        z = zero(x) * Δ
-        if insupport
-            c = Δ / diff
-            return c, -c, z
-        else
-            c = Δ / one(diff)
-            cNaN = oftype(c, NaN)
-            return cNaN, cNaN, oftype(z, NaN)
+logpdf(d::Uniform, x::TrackedReal) = track(uniformlogpdf, d.a, d.b, x)
+logpdf(d::Uniform{<:TrackedReal}, x::Real) = track(uniformlogpdf, d.a, d.b, x)
+logpdf(d::Uniform{<:TrackedReal}, x::TrackedReal) = track(uniformlogpdf, d.a, d.b, x)
+
+# avoid any possible promotions of the outer constructor
+uniformlogpdf(a::T, b::T, x::Real) where {T<:Real} = logpdf(Uniform{T}(a, b), x)
+@grad function uniformlogpdf(_a::T, _b::T, _x::Real) where {T<:Real}
+    # Compute log probability
+    a = data(_a)
+    b = data(_b)
+    x = data(_x)
+    insupport = a <= x <= b
+    diff = b - a
+    Ω = insupport ? -log(diff) : log(zero(diff))
+
+    # Define pullback
+    function uniformlogpdf_pullback(Δ)
+        Δa = Δ / diff
+        if !insupport
+            Δa = zero(Δa)
         end
+        return Δa, -Δa, zero(x)
     end
 
-    return lp, pullback
+    return Ω, uniformlogpdf_pullback
 end
 
-
 ## Binomial ##
 
 binomlogpdf(n::Int, p::TrackedReal, x::Int) = track(binomlogpdf, n, p, x)
diff --git a/src/univariate.jl b/src/univariate.jl
index baab8c5..82b8d66 100644
--- a/src/univariate.jl
+++ b/src/univariate.jl
@@ -1,31 +1,3 @@
-## Uniform ##
-
-struct TuringUniform{T} <: ContinuousUnivariateDistribution
-    a::T
-    b::T
-end
-TuringUniform() = TuringUniform(0.0, 1.0)
-function TuringUniform(a::Int, b::Int)
-    return TuringUniform{Float64}(Float64(a), Float64(b))
-end
-function TuringUniform(a::Real, b::Real)
-    T = promote_type(typeof(a), typeof(b))
-    return TuringUniform{T}(T(a), T(b))
-end
-Distributions.logpdf(d::TuringUniform, x::Real) = uniformlogpdf(d.a, d.b, x)
-
-Base.minimum(d::TuringUniform) = d.a
-Base.maximum(d::TuringUniform) = d.b
-
-function uniformlogpdf(a, b, x)
-    diff = b - a
-    if a <= x <= b
-        return -log(diff)
-    else
-        return log(zero(diff))
-    end
-end
-
 ## PoissonBinomial ##
 
 struct TuringPoissonBinomial{T<:Real, TV1<:AbstractVector{T}, TV2<:AbstractVector} <: DiscreteUnivariateDistribution
diff --git a/src/zygote.jl b/src/zygote.jl
index 5500e8e..e7dec8e 100644
--- a/src/zygote.jl
+++ b/src/zygote.jl
@@ -1,9 +1,3 @@
-## Uniform ##
-
-ZygoteRules.@adjoint function Distributions.Uniform(args...)
-    return ZygoteRules.pullback(TuringUniform, args...)
-end
-
 ## Product
 
 # Tests with `Kolmogorov` seem to fail otherwise?!
diff --git a/test/ad/chainrules.jl b/test/ad/chainrules.jl
deleted file mode 100644
index 9496ba2..0000000
--- a/test/ad/chainrules.jl
+++ /dev/null
@@ -1,7 +0,0 @@
-@testset "chainrules" begin
-    x = randn()
-    z = x + exp(randn())
-    y = z + exp(randn())
-    test_frule(DistributionsAD.uniformlogpdf, x, y, z)
-    test_rrule(DistributionsAD.uniformlogpdf, x, y, z)
-end
diff --git a/test/ad/distributions.jl b/test/ad/distributions.jl
index 08ddb92..ef5ee18 100644
--- a/test/ad/distributions.jl
+++ b/test/ad/distributions.jl
@@ -201,9 +201,6 @@
         DistSpec(Uniform, (), 0.5),
         DistSpec(Uniform, (alpha, alpha + beta), alpha + beta * gamma),
 
-        DistSpec(TuringUniform, (), 0.5),
-        DistSpec(TuringUniform, (alpha, alpha + beta), alpha + beta * gamma),
-
         DistSpec(VonMises, (), 1.0),
 
         DistSpec(Weibull, (), 1.0),
diff --git a/test/ad/others.jl b/test/ad/others.jl
index a0b7431..1c70558 100644
--- a/test/ad/others.jl
+++ b/test/ad/others.jl
@@ -1,9 +1,5 @@
 @testset "AD: Others" begin
     if GROUP == "All" || GROUP == "Tracker"
-        @testset "TuringUniform" begin
-            @test logpdf(TuringUniform(), param(0.5)) == 0
-        end
-
         @testset "Semicircle" begin
             @test Tracker.data(logpdf(Semicircle(1.0), param(0.5))) == logpdf(Semicircle(1.0), 0.5)
         end
@@ -17,7 +13,7 @@
     @testset "zygote_ldiv" begin
         A = to_posdef(rand(3, 3))
         B = to_posdef(rand(3, 3))
-        
+
         test_reverse_mode_ad(randn(3, 3), A, B) do A, B
             return DistributionsAD.zygote_ldiv(A, B)
         end
@@ -84,10 +80,10 @@
                     v = rand(rng, T, n)
                     d = rand(Int, n)
                     tp = ReverseDiff.InstructionTape()
-                    x = ReverseDiff.TrackedArray(v, d, tp) 
+                    x = ReverseDiff.TrackedArray(v, d, tp)
                     test_adapt_randn(rng, x, T, dims...)
                 end
             end
         end
     end
-end
\ No newline at end of file
+end
diff --git a/test/others.jl b/test/others.jl
index 10bd450..23549ae 100644
--- a/test/others.jl
+++ b/test/others.jl
@@ -96,10 +96,6 @@
         end
     end
 
-    @testset "TuringUniform" begin
-        @test logpdf(TuringUniform(), 0.5) == 0
-    end
-
     @testset "TuringPoissonBinomial" begin
         d1 = TuringPoissonBinomial([0.5, 0.5])
         d2 = PoissonBinomial([0.5, 0.5])
diff --git a/test/runtests.jl b/test/runtests.jl
index d03627e..3829094 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -7,7 +7,7 @@ using PDMats
 using Random, LinearAlgebra, Test
 
 using Distributions: meanlogdet
-using DistributionsAD: TuringUniform, TuringMvNormal, TuringMvLogNormal,
+using DistributionsAD: TuringMvNormal, TuringMvLogNormal,
                        TuringPoissonBinomial, TuringDirichlet
 using StatsBase: entropy
 using StatsFuns: StatsFuns, logsumexp, logistic
@@ -25,6 +25,5 @@ end
 if GROUP == "All" || GROUP in ("ForwardDiff", "Zygote", "ReverseDiff", "Tracker")
     include("ad/utils.jl")
     include("ad/others.jl")
-    include("ad/chainrules.jl")
     include("ad/distributions.jl")
 end