diff --git a/Project.toml b/Project.toml
index 5a5429aa..341f3699 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "TemporalGPs"
 uuid = "e155a3c4-0841-43e1-8b83-a0e4f03cc18f"
 authors = ["willtebbutt <wt0881@my.bristol.ac.uk>"]
-version = "0.5.1"
+version = "0.5.2"
 
 [deps]
 AbstractGPs = "99985d1d-32ba-4be9-9821-2ec096f28918"
diff --git a/src/gp/lti_sde.jl b/src/gp/lti_sde.jl
index 2d950c75..c26ea0e4 100644
--- a/src/gp/lti_sde.jl
+++ b/src/gp/lti_sde.jl
@@ -246,7 +246,25 @@ Zygote.@adjoint function stationary_distribution(k::Matern52Kernel, storage_type
     return stationary_distribution(k, storage_type), Δ->(nothing, nothing)
 end
 
+# Constant
 
+function TemporalGPs.to_sde(k::ConstantKernel, ::SArrayStorage{T}) where {T<:Real}
+    F = SMatrix{1, 1, T}(0)
+    q = convert(T, 0)
+    H = SVector{1, T}(1)
+    return F, q, H
+end
+
+function TemporalGPs.stationary_distribution(k::ConstantKernel, ::SArrayStorage{T}) where {T<:Real}
+    return TemporalGPs.Gaussian(
+        SVector{1, T}(0),
+        SMatrix{1, 1, T}( T(only(k.c)) ),
+    )
+end
+
+Zygote.@adjoint function to_sde(k::ConstantKernel, storage_type)
+    return to_sde(k, storage_type), Δ->(nothing, nothing)
+end
 
 # Scaled
 
diff --git a/src/util/zygote_rules.jl b/src/util/zygote_rules.jl
index a0a7b9a6..0ad8797b 100644
--- a/src/util/zygote_rules.jl
+++ b/src/util/zygote_rules.jl
@@ -38,11 +38,11 @@ end
     return SMatrix{D1, D2}(X), SMatrix_pullback
 end
 
-@adjoint function SMatrix{1, 1}(a)
-    SMatrix_pullback(Δ::AbstractMatrix) = (first(Δ), )
+function Zygote._pullback(::AContext, ::Type{<:SMatrix{1, 1}}, a)
+    SMatrix_pullback(::Nothing) = nothing
+    SMatrix_pullback(Δ::AbstractMatrix) = (nothing, first(Δ), )
     return SMatrix{1, 1}(a), SMatrix_pullback
 end
-
 # Implementation of the matrix exponential that assumes one doesn't require access to the
 # gradient w.r.t. `A`, only `t`. The former is a bit compute-intensive to get at, while the
 # latter is very cheap.
diff --git a/test/gp/lti_sde.jl b/test/gp/lti_sde.jl
index 44479e0e..3e22dd67 100644
--- a/test/gp/lti_sde.jl
+++ b/test/gp/lti_sde.jl
@@ -26,7 +26,7 @@ println("lti_sde:")
             # (name="static storage Float32", val=SArrayStorage(Float32)),
         )
 
-        kernels = [Matern12Kernel(), Matern32Kernel(), Matern52Kernel()]
+        kernels = [Matern12Kernel(), Matern32Kernel(), Matern52Kernel(), ConstantKernel(c=1.5)]
 
         @testset "$kernel, $(storage.name)" for kernel in kernels, storage in storages
             F, q, H = TemporalGPs.to_sde(kernel, storage.val)