diff --git a/src/host/linalg.jl b/src/host/linalg.jl
index a198c3de..3c6788e2 100644
--- a/src/host/linalg.jl
+++ b/src/host/linalg.jl
@@ -326,6 +326,14 @@ end
 
 Base.copy(D::Diagonal{T, <:AbstractGPUArray{T, N}}) where {T, N} = Diagonal(copy(D.diag))
 
+# copy only the diagonal; the generic `AnyGPUArray` method would launch a kernel over all
+# n^2 entries, calling `setindex!(::Diagonal, ...)` whose error path isn't GPU-compatible
+function Base.copyto!(D1::Diagonal{T, <:AbstractGPUArray{T, N}},
+                      D2::Diagonal{S, <:AbstractGPUArray{S, M}}) where {T, N, S, M}
+    copyto!(D1.diag, D2.diag)
+    return D1
+end
+
 _isrealandpositive(x) = isreal(x) && real(x) > 0
 
 function LinearAlgebra.cholesky!(D::Diagonal{<:Any, <:AbstractGPUArray},
diff --git a/test/testsuite/linalg.jl b/test/testsuite/linalg.jl
index 0df896c7..6a3835b1 100644
--- a/test/testsuite/linalg.jl
+++ b/test/testsuite/linalg.jl
@@ -512,6 +512,18 @@ end
         @test collect(D) == collect(C)
     end
 
+    @testset "copyto! diagonal" begin
+        D = Diagonal(AT(rand(Float32, 10)))
+        C = Diagonal(AT(zeros(Float32, 10)))
+        @test copyto!(C, D) === C
+        @test C.diag isa AT
+        @test collect(C) == collect(D)
+
+        D = Diagonal(AT(Int32.(1:10)))
+        copyto!(C, D)
+        @test collect(C) == Diagonal(Float32.(1:10))
+    end
+
     @testset "cholesky + Diagonal" begin
         n = 128
         # Add one in order prevent failures due to random numbers being zero