diff --git a/Project.toml b/Project.toml
index 396e917..39688f5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,13 +1,14 @@
 name = "DiagonalArrays"
 uuid = "74fd4be6-21e2-4f6f-823a-4360d37c7a77"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.3.14"
+version = "0.3.15"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
 DerivableInterfaces = "6c5e35bf-e59e-4898-b73c-732dcc4ba65f"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+MapBroadcast = "ebd9b9da-f48d-417c-9660-449667d60261"
 SparseArraysBase = "0d5efcca-f356-4864-8770-e1ed8d78f208"
 
 [compat]
@@ -15,5 +16,6 @@ ArrayLayouts = "1.10.4"
 DerivableInterfaces = "0.5.5"
 FillArrays = "1.13.0"
 LinearAlgebra = "1.10.0"
+MapBroadcast = "0.1.10"
 SparseArraysBase = "0.7.2"
 julia = "1.10"
diff --git a/src/abstractdiagonalarray/diagonalarraydiaginterface.jl b/src/abstractdiagonalarray/diagonalarraydiaginterface.jl
index 7b2d389..3f914d3 100644
--- a/src/abstractdiagonalarray/diagonalarraydiaginterface.jl
+++ b/src/abstractdiagonalarray/diagonalarraydiaginterface.jl
@@ -30,10 +30,6 @@ struct DiagonalArrayStyle{N} <: AbstractDiagonalArrayStyle{N} end
 
 DiagonalArrayStyle{M}(::Val{N}) where {M,N} = DiagonalArrayStyle{N}()
 
-@interface ::AbstractDiagonalArrayInterface function Broadcast.BroadcastStyle(type::Type)
-  return DiagonalArrayStyle{ndims(type)}()
-end
-
 function SparseArraysBase.isstored(
   a::AbstractDiagonalArray{<:Any,N}, I::Vararg{Int,N}
 ) where {N}
@@ -81,6 +77,29 @@ function Base.setindex!(a::AbstractDiagonalArray, value, I::DiagIndex)
   return invoke(setindex!, Tuple{AbstractArray,Any,DiagIndex}, a, value, I)
 end
 
+@interface ::AbstractDiagonalArrayInterface function Broadcast.BroadcastStyle(type::Type)
+  return DiagonalArrayStyle{ndims(type)}()
+end
+
+using Base.Broadcast: Broadcasted, broadcasted
+using MapBroadcast: Mapped
+# Map to a flattened broadcast expression of the diagonals of the arrays,
+# also checking that the function preserves zeros.
+function broadcasted_diagview(bc::Broadcasted)
+  m = Mapped(bc)
+  iszero(m.f(map(zero ∘ eltype, m.args)...)) || error(
+    "Broadcasting DiagonalArrays with function that doesn't preserve zeros isn't supported yet.",
+  )
+  return broadcasted(m.f, map(diagview, m.args)...)
+end
+function Base.copy(bc::Broadcasted{<:DiagonalArrayStyle})
+  return DiagonalArray(copy(broadcasted_diagview(bc)), axes(bc))
+end
+function Base.copyto!(dest::AbstractArray, bc::Broadcasted{<:DiagonalArrayStyle})
+  copyto!(diagview(dest), broadcasted_diagview(bc))
+  return dest
+end
+
 ## SparseArraysBase.StorageIndex(i::DiagIndex) = StorageIndex(index(i))
 
 ## function Base.getindex(a::AbstractDiagonalArray, i::DiagIndex)
diff --git a/src/diagonalarray/delta.jl b/src/diagonalarray/delta.jl
index b2dc860..f91e312 100644
--- a/src/diagonalarray/delta.jl
+++ b/src/diagonalarray/delta.jl
@@ -1,6 +1,25 @@
-using FillArrays: Ones, OnesVector
+using FillArrays: AbstractFillVector, Ones, OnesVector
+
+const ScaledDelta{T,N,Diag<:AbstractFillVector{T},Unstored<:AbstractArray{T,N}} = DiagonalArray{
+  T,N,Diag,Unstored
+}
+const ScaledDeltaVector{T,Diag<:AbstractFillVector{T},Unstored<:AbstractVector{T}} = DiagonalVector{
+  T,Diag,Unstored
+}
+const ScaledDeltaMatrix{T,Diag<:AbstractFillVector{T},Unstored<:AbstractMatrix{T}} = DiagonalMatrix{
+  T,Diag,Unstored
+}
+
+const Delta{T,N,Diag<:OnesVector{T},Unstored<:AbstractArray{T,N}} = DiagonalArray{
+  T,N,Diag,Unstored
+}
+const DeltaVector{T,Diag<:OnesVector{T},Unstored<:AbstractVector{T}} = DiagonalVector{
+  T,Diag,Unstored
+}
+const DeltaMatrix{T,Diag<:OnesVector{T},Unstored<:AbstractMatrix{T}} = DiagonalMatrix{
+  T,Diag,Unstored
+}
 
-const Delta{T,N,V<:OnesVector{T},Axes} = DiagonalArray{T,N,V,Axes}
 function Delta{T}(
   ax::Tuple{AbstractUnitRange{<:Integer},Vararg{AbstractUnitRange{<:Integer}}}
 ) where {T}
diff --git a/src/diagonalarray/diagonalmatrix.jl b/src/diagonalarray/diagonalmatrix.jl
index 9c77c25..2fff225 100644
--- a/src/diagonalarray/diagonalmatrix.jl
+++ b/src/diagonalarray/diagonalmatrix.jl
@@ -1,11 +1,6 @@
-const DiagonalMatrix{T,Diag,Zero} = DiagonalArray{T,2,Diag,Zero}
-
-function DiagonalMatrix(diag::AbstractVector)
-  return DiagonalArray{<:Any,2}(diag)
-end
-function DiagonalMatrix(diag::AbstractVector, ax::Tuple)
-  return DiagonalArray{<:Any,2}(diag, ax)
-end
+const DiagonalMatrix{T,Diag<:AbstractVector{T},Unstored<:AbstractMatrix{T}} = DiagonalArray{
+  T,2,Diag,Unstored
+}
 
 # LinearAlgebra
 
diff --git a/src/diagonalarray/diagonalvector.jl b/src/diagonalarray/diagonalvector.jl
index 40e35e4..ec3cde8 100644
--- a/src/diagonalarray/diagonalvector.jl
+++ b/src/diagonalarray/diagonalvector.jl
@@ -1,4 +1,6 @@
-const DiagonalVector{T,Diag,Zero} = DiagonalArray{T,1,Diag,Zero}
+const DiagonalVector{T,Diag<:AbstractVector{T},Unstored<:AbstractVector{T}} = DiagonalArray{
+  T,1,Diag,Unstored
+}
 
 function DiagonalVector(diag::AbstractVector)
   return DiagonalArray{<:Any,1}(diag)
diff --git a/test/test_basics.jl b/test/test_basics.jl
index a7f1c00..dbc5f16 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -3,8 +3,11 @@ using DerivableInterfaces: permuteddims
 using DiagonalArrays:
   DiagonalArrays,
   Delta,
+  DeltaMatrix,
   DiagonalArray,
   DiagonalMatrix,
+  ScaledDelta,
+  ScaledDeltaMatrix,
   δ,
   delta,
   diagindices,
@@ -116,6 +119,22 @@ using LinearAlgebra: Diagonal, mul!
       @test diagview(b) ≡ diagview(a)
       @test size(b) === (4, 2, 3)
     end
+    @testset "Broadcasting" begin
+      a = DiagonalArray(randn(elt, 2), (2, 3))
+      b = DiagonalArray(randn(elt, 2), (2, 3))
+      c = a .+ 2 .* b
+      @test c ≈ Array(a) + 2 * Array(b)
+      # Non-zero-preserving functions not supported yet.
+      @test_broken a .+ 2
+
+      c = DiagonalArray{elt}(undef, (2, 3))
+      c .= a .+ 2 .* b
+      @test c ≈ Array(a) + 2 * Array(b)
+
+      # Non-zero-preserving functions not supported yet.
+      c = DiagonalArray{elt}(undef, (2, 3))
+      @test_broken c .= a .+ 2
+    end
     @testset "Matrix multiplication" begin
       a1 = DiagonalArray{elt}(undef, (2, 3))
       a1[1, 1] = 11
@@ -197,7 +216,9 @@ using LinearAlgebra: Diagonal, mul!
         @test eltype(a) === elt′
         @test diaglength(a) == 2
         @test a isa DiagonalArray{elt′,2}
+        @test a isa DiagonalMatrix{elt′}
         @test a isa Delta{elt′,2}
+        @test a isa DeltaMatrix{elt′}
         @test size(a) == (2, 2)
         @test diaglength(a) == 2
         @test storedlength(a) == 2
@@ -211,11 +232,17 @@ using LinearAlgebra: Diagonal, mul!
         # TODO: Fix this. Mapping doesn't preserve
         # the diagonal structure properly.
         # https://github.com/ITensor/DiagonalArrays.jl/issues/7
-        @test_broken diagview(a′) isa Fill
+        @test diagview(a′) isa Fill{promote_type(Int, elt′)}
+        @test a′ isa ScaledDelta{promote_type(Int, elt′),2}
+        @test a′ isa ScaledDeltaMatrix{promote_type(Int, elt′)}
 
         b = randn(elt, (2, 3))
         a_dest = a * b
         @test a_dest ≈ Array(a) * Array(b)
+
+        a_dest = a * a
+        @test a_dest ≈ Array(a) * Array(a)
+        @test diagview(a_dest) isa Ones{elt′}
       end
     end
   end