diff --git a/Project.toml b/Project.toml
index a442357..280bead 100644
--- a/Project.toml
+++ b/Project.toml
@@ -15,10 +15,12 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 [weakdeps]
 ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
 InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [extensions]
 ChangesOfVariablesExt = "ChangesOfVariables"
 InverseFunctionsExt = "InverseFunctions"
+UnitfulExt = "Unitful"
 
 [compat]
 ArgCheck = "1, 2"
@@ -30,4 +32,5 @@ LinearAlgebra = "1.6"
 LogExpFunctions = "0.3"
 Random = "1.6"
 StaticArrays = "1"
+Unitful = "1"
 julia = "1.10"
diff --git a/ext/UnitfulExt.jl b/ext/UnitfulExt.jl
new file mode 100644
index 0000000..8f2c9ba
--- /dev/null
+++ b/ext/UnitfulExt.jl
@@ -0,0 +1,105 @@
+module UnitfulExt
+
+using ArgCheck: @argcheck
+using DocStringExtensions: FUNCTIONNAME, SIGNATURES, TYPEDEF
+using LogExpFunctions: logistic, logit
+import Unitful: Quantity, Units, ustrip, NoUnits
+import TransformVariables: ScalarTransform, transform, transform_and_logjac, inverse, as, Infinity, asℝ₊
+
+
+####
+#### shifted exponential with units
+####
+"""
+$(TYPEDEF)
+
+Shifted exponential with units. When `D::Bool == true`, maps to `(shift, ∞)` using `x ↦
+shift + eˣ`, otherwise to `(-∞, shift)` using `x ↦ shift - eˣ`.
+"""
+struct DimShiftedExp{D, T <: Quantity} <: ScalarTransform
+    shift::T
+    function DimShiftedExp{D,T}(shift::T) where {D, T <: Quantity}
+        @argcheck D isa Bool
+        new(shift)
+    end
+end
+
+DimShiftedExp(D::Bool, shift::T) where {T <: Quantity} = DimShiftedExp{D,T}(shift)
+
+transform(t::DimShiftedExp{D, Quantity{V,DD,U}}, x::Real) where {D, V, DD, U} =
+    D ? t.shift + exp(x)*U() : t.shift - exp(x)*U()
+
+# NOTE: not sure if or how this should be defined, since units.
+# transform_and_logjac(t::DimShiftedExp, x::Real) = transform(t, x), x
+
+function inverse(t::DimShiftedExp{D, Quantity{V,DD,U}}, x::Quantity) where {D, V, DD, U}
+    (; shift) = t
+    if D
+        @argcheck x > shift DomainError
+        log(ustrip(U(), x - shift))
+    else
+        @argcheck x < shift DomainError
+        log(ustrip(U(), shift - x))
+    end
+end
+
+###
+#### scaled-shifted logistic with units
+####
+
+"""
+$(TYPEDEF)
+
+Maps to `(scale, shift + scale)` using `logistic(x) * scale + shift`.
+"""
+struct DimScaledShiftedLogistic{T <: Quantity} <: ScalarTransform
+    scale::T
+    shift::T
+    function DimScaledShiftedLogistic{T}(scale::T, shift::T) where {T <: Quantity}
+        @argcheck scale > zero(typeof(scale))
+        new(scale, shift)
+    end
+end
+
+DimScaledShiftedLogistic(scale::T, shift::T) where {T <: Quantity} =
+    DimScaledShiftedLogistic{T}(scale, shift)
+
+function DimScaledShiftedLogistic(scale::T1, shift::T2) where {T1 <: Quantity, T2 <: Quantity}
+    DimScaledShiftedLogistic(promote(scale, shift)...)
+end
+
+# # Switch to muladd and now it does have a DiffRule defined
+transform(t::DimScaledShiftedLogistic, x::Real) = muladd(logistic(x), t.scale, t.shift)
+
+# NOTE: not sure if or how this should be defined, since units.
+# transform_and_logjac(t::ScaledShiftedLogistic, x) =
+#     transform(t, x), log(t.scale) + logistic_logjac(x)
+
+function inverse(t::DimScaledShiftedLogistic{Quantity{N,D,U}}, y) where {N,D,U}
+    @argcheck y > t.shift           DomainError
+    @argcheck y < t.scale + t.shift DomainError
+    logit(ustrip(NoUnits, (y - t.shift)/t.scale))
+end
+
+# NOTE: not sure if or how this should be defined, since units.
+# # NOTE: inverse_and_logjac interface experimental and sporadically implemented for now
+# function inverse_and_logjac(t::ScaledShiftedLogistic, y)
+#     @argcheck y > t.shift           DomainError
+#     @argcheck y < t.scale + t.shift DomainError
+#     z = (y - t.shift) / t.scale
+#     logit(z), logit_logjac(z) - log(t.scale)
+# end
+
+function as(::Type{Real}, left::Quantity, right::Quantity)
+    @argcheck left < right "the interval ($(left), $(right)) is empty"
+    DimScaledShiftedLogistic(right - left, left)
+end
+
+as(::Type{Real}, left::Quantity, ::Infinity{true}) = DimShiftedExp(true, left)
+
+as(::Type{Real}, ::Infinity{false}, right::Quantity) = DimShiftedExp(false, right)
+
+Base.:(*)(a::typeof(asℝ₊), u::Units) = as(Real, 0.0*u, Infinity{true}())
+Base.:(*)(a::typeof(asℝ₋), u::Units) = as(Real, Infinity{false}(), 0.0*u)
+
+end # module
\ No newline at end of file
diff --git a/test/Project.toml b/test/Project.toml
index bfaad77..e26b067 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -13,3 +13,4 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TransformedLogDensities = "f9bc47f6-f3f8-4f3b-ab21-f8bc73906f26"
+Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
diff --git a/test/runtests.jl b/test/runtests.jl
index f972660..a0edccb 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -8,6 +8,7 @@ using TransformVariables:
     unit_triangular_dimension, logistic, logistic_logjac, logit, inverse_and_logjac,
     NOLOGJAC, transform_with
 import ChangesOfVariables, InverseFunctions
+import Unitful: @u_str, ustrip
 using Enzyme: autodiff, ReverseWithPrimal, Active, Const
 
 const CIENV = get(ENV, "CI", "") == "true"
@@ -598,6 +599,46 @@ end
     InverseFunctions.test_inverse(inv_f, 1.7)
 end
 
+@testset "Unitful" begin
+    @testset "finite" begin
+        t = as(Real, 0.0u"s", 2u"hr")
+        f = transform(t)
+        inv_f = inverse(t)
+        q = transform(t, 1.0)
+        @test ustrip(u"s", q) > 0
+        @test_throws DomainError inverse(t, -1.0u"s")
+        @test_throws DomainError inverse(t, 3u"hr")
+        InverseFunctions.test_inverse(f, -4.2)
+        InverseFunctions.test_inverse(inv_f, 1.7u"s")
+    end
+
+    @testset "positive real" begin
+        t = as(Real, -1.0u"s", ∞)
+        f = transform(t)
+        inv_f = inverse(t)
+        q = transform(t, 1.0)
+        @test q ≈ exp(1.0)*u"s" - 1.0u"s"
+        @test ustrip(u"s", q) > -1
+        @test_throws DomainError inverse(t, -2.0u"s")
+        InverseFunctions.test_inverse(f, -4.2)
+        InverseFunctions.test_inverse(inv_f, 1.7u"s")
+    end
+
+    @testset "negative real" begin
+        t = as(Real, -∞, 1.0u"s")
+        f = transform(t)
+        inv_f = inverse(t)
+        q = transform(t, 2.0)
+        @test q ≈ -exp(2.0)*u"s" + 1.0u"s"
+        @test ustrip(u"s", q) < 1
+        @test_throws DomainError inverse(t, 2.0u"s")
+        InverseFunctions.test_inverse(f, -4.2)
+        InverseFunctions.test_inverse(inv_f, -1.7u"s")
+    end
+end
+
+
+
 @testset "as static array" begin
     S = Tuple{2,3,4}
     t = as(SArray{S})