diff --git a/src/ApproximateGPs.jl b/src/ApproximateGPs.jl
index 029be317..97a9d29b 100644
--- a/src/ApproximateGPs.jl
+++ b/src/ApproximateGPs.jl
@@ -23,4 +23,10 @@ include("deprecations.jl")
 
 include("TestUtils.jl")
 
+import ChainRulesCore: ProjectTo, Tangent
+using PDMats: ScalMat
+ProjectTo(x::T) where {T<:ScalMat} = ProjectTo{T}(; dim=x.dim, value=ProjectTo(x.value))
+(pr::ProjectTo{<:ScalMat})(dx::ScalMat) = ScalMat(pr.dim, pr.value(dx.value))
+(pr::ProjectTo{<:ScalMat})(dx::Tangent{<:ScalMat}) = ScalMat(pr.dim, pr.value(dx.value))
+
 end