diff --git a/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/sparsearrayinterface.jl b/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/sparsearrayinterface.jl
index 98095225f7..e4929b5e81 100644
--- a/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/sparsearrayinterface.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/src/abstractsparsearray/sparsearrayinterface.jl
@@ -32,7 +32,7 @@ end
 
 # TODO: Make this into a generic definition of all `AbstractArray`?
 function SparseArrayInterface.stored_indices(
-  a::PermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:AbstractSparseArray}
+  a::AnyPermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:AbstractSparseArray}
 )
   return Iterators.map(
     I -> CartesianIndex(map(i -> I[i], perm(a))), stored_indices(parent(a))
@@ -41,7 +41,7 @@ end
 
 # TODO: Make this into a generic definition of all `AbstractArray`?
 function SparseArrayInterface.sparse_storage(
-  a::PermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:AbstractSparseArray}
+  a::AnyPermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:AbstractSparseArray}
 )
   return sparse_storage(parent(a))
 end
diff --git a/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/wrappers.jl b/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/wrappers.jl
index b4364b80ed..a4fce3bb0c 100644
--- a/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/wrappers.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/src/sparsearrayinterface/wrappers.jl
@@ -1,19 +1,26 @@
+using ..NestedPermutedDimsArrays: NestedPermutedDimsArray
+
 ## PermutedDimsArray
 
-perm(::PermutedDimsArray{<:Any,<:Any,P}) where {P} = P
-iperm(::PermutedDimsArray{<:Any,<:Any,<:Any,IP}) where {IP} = IP
+const AnyPermutedDimsArray{T,N,perm,iperm,P} = Union{
+  PermutedDimsArray{T,N,perm,iperm,P},NestedPermutedDimsArray{T,N,perm,iperm,P}
+}
+
+# TODO: Use `TypeParameterAccessors`.
+perm(::AnyPermutedDimsArray{<:Any,<:Any,Perm}) where {Perm} = Perm
+iperm(::AnyPermutedDimsArray{<:Any,<:Any,<:Any,IPerm}) where {IPerm} = IPerm
 
 # TODO: Use `Base.PermutedDimsArrays.genperm` or
 # https://github.com/jipolanco/StaticPermutations.jl?
 genperm(v, perm) = map(j -> v[j], perm)
 genperm(v::CartesianIndex, perm) = CartesianIndex(map(j -> Tuple(v)[j], perm))
 
-function storage_index_to_index(a::PermutedDimsArray, I)
+function storage_index_to_index(a::AnyPermutedDimsArray, I)
   return genperm(storage_index_to_index(parent(a), I), perm(a))
 end
 
 function index_to_storage_index(
-  a::PermutedDimsArray{<:Any,N}, I::CartesianIndex{N}
+  a::AnyPermutedDimsArray{<:Any,N}, I::CartesianIndex{N}
 ) where {N}
   return index_to_storage_index(parent(a), genperm(I, perm(a)))
 end
diff --git a/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/AbstractSparseArrays.jl b/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/AbstractSparseArrays.jl
index 1455b65c15..1a81334397 100644
--- a/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/AbstractSparseArrays.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/AbstractSparseArrays.jl
@@ -1,24 +1,29 @@
 module AbstractSparseArrays
 using ArrayLayouts: ArrayLayouts, MatMulMatAdd, MemoryLayout, MulAdd
-using NDTensors.SparseArrayInterface: SparseArrayInterface, AbstractSparseArray
+using NDTensors.SparseArrayInterface: SparseArrayInterface, AbstractSparseArray, Zero
 
-struct SparseArray{T,N} <: AbstractSparseArray{T,N}
+struct SparseArray{T,N,Zero} <: AbstractSparseArray{T,N}
   data::Vector{T}
   dims::Tuple{Vararg{Int,N}}
   index_to_dataindex::Dict{CartesianIndex{N},Int}
   dataindex_to_index::Vector{CartesianIndex{N}}
+  zero::Zero
 end
-function SparseArray{T,N}(dims::Tuple{Vararg{Int,N}}) where {T,N}
-  return SparseArray{T,N}(
-    T[], dims, Dict{CartesianIndex{N},Int}(), Vector{CartesianIndex{N}}()
+function SparseArray{T,N}(dims::Tuple{Vararg{Int,N}}; zero=Zero()) where {T,N}
+  return SparseArray{T,N,typeof(zero)}(
+    T[], dims, Dict{CartesianIndex{N},Int}(), Vector{CartesianIndex{N}}(), zero
   )
 end
-SparseArray{T,N}(dims::Vararg{Int,N}) where {T,N} = SparseArray{T,N}(dims)
-SparseArray{T}(dims::Tuple{Vararg{Int}}) where {T} = SparseArray{T,length(dims)}(dims)
-function SparseArray{T}(::UndefInitializer, dims::Tuple{Vararg{Int}}) where {T}
-  return SparseArray{T}(dims)
+function SparseArray{T,N}(dims::Vararg{Int,N}; kwargs...) where {T,N}
+  return SparseArray{T,N}(dims; kwargs...)
 end
-SparseArray{T}(dims::Vararg{Int}) where {T} = SparseArray{T}(dims)
+function SparseArray{T}(dims::Tuple{Vararg{Int}}; kwargs...) where {T}
+  return SparseArray{T,length(dims)}(dims; kwargs...)
+end
+function SparseArray{T}(::UndefInitializer, dims::Tuple{Vararg{Int}}; kwargs...) where {T}
+  return SparseArray{T}(dims; kwargs...)
+end
+SparseArray{T}(dims::Vararg{Int}; kwargs...) where {T} = SparseArray{T}(dims; kwargs...)
 
 # ArrayLayouts interface
 struct SparseLayout <: MemoryLayout end
@@ -41,6 +46,7 @@ function Base.similar(a::SparseArray, elt::Type, dims::Tuple{Vararg{Int}})
 end
 
 # Minimal interface
+SparseArrayInterface.getindex_zero_function(a::SparseArray) = a.zero
 SparseArrayInterface.sparse_storage(a::SparseArray) = a.data
 function SparseArrayInterface.index_to_storage_index(
   a::SparseArray{<:Any,N}, I::CartesianIndex{N}
diff --git a/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl b/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl
index e1ca4f0661..f74846e2c1 100644
--- a/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/test/SparseArrayInterfaceTestUtils/SparseArrays.jl
@@ -1,24 +1,29 @@
 module SparseArrays
 using LinearAlgebra: LinearAlgebra
-using NDTensors.SparseArrayInterface: SparseArrayInterface
+using NDTensors.SparseArrayInterface: SparseArrayInterface, Zero
 
-struct SparseArray{T,N} <: AbstractArray{T,N}
+struct SparseArray{T,N,Zero} <: AbstractArray{T,N}
   data::Vector{T}
   dims::Tuple{Vararg{Int,N}}
   index_to_dataindex::Dict{CartesianIndex{N},Int}
   dataindex_to_index::Vector{CartesianIndex{N}}
+  zero::Zero
 end
-function SparseArray{T,N}(dims::Tuple{Vararg{Int,N}}) where {T,N}
-  return SparseArray{T,N}(
-    T[], dims, Dict{CartesianIndex{N},Int}(), Vector{CartesianIndex{N}}()
+function SparseArray{T,N}(dims::Tuple{Vararg{Int,N}}; zero=Zero()) where {T,N}
+  return SparseArray{T,N,typeof(zero)}(
+    T[], dims, Dict{CartesianIndex{N},Int}(), Vector{CartesianIndex{N}}(), zero
   )
 end
-SparseArray{T,N}(dims::Vararg{Int,N}) where {T,N} = SparseArray{T,N}(dims)
-SparseArray{T}(dims::Tuple{Vararg{Int}}) where {T} = SparseArray{T,length(dims)}(dims)
-function SparseArray{T}(::UndefInitializer, dims::Tuple{Vararg{Int}}) where {T}
-  return SparseArray{T}(dims)
+function SparseArray{T,N}(dims::Vararg{Int,N}; kwargs...) where {T,N}
+  return SparseArray{T,N}(dims; kwargs...)
 end
-SparseArray{T}(dims::Vararg{Int}) where {T} = SparseArray{T}(dims)
+function SparseArray{T}(dims::Tuple{Vararg{Int}}; kwargs...) where {T}
+  return SparseArray{T,length(dims)}(dims; kwargs...)
+end
+function SparseArray{T}(::UndefInitializer, dims::Tuple{Vararg{Int}}; kwargs...) where {T}
+  return SparseArray{T}(dims; kwargs...)
+end
+SparseArray{T}(dims::Vararg{Int}; kwargs...) where {T} = SparseArray{T}(dims; kwargs...)
 
 # LinearAlgebra interface
 function LinearAlgebra.mul!(
@@ -53,6 +58,7 @@ function Base.fill!(a::SparseArray, value)
 end
 
 # Minimal interface
+SparseArrayInterface.getindex_zero_function(a::SparseArray) = a.zero
 SparseArrayInterface.sparse_storage(a::SparseArray) = a.data
 function SparseArrayInterface.index_to_storage_index(
   a::SparseArray{<:Any,N}, I::CartesianIndex{N}
@@ -79,6 +85,33 @@ function SparseArrayInterface.stored_indices(
   )
 end
 
+# TODO: Make this into a generic definition of all `AbstractArray`?
+using NDTensors.SparseArrayInterface: sparse_storage
+function SparseArrayInterface.sparse_storage(
+  a::PermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:SparseArray}
+)
+  return sparse_storage(parent(a))
+end
+
+# TODO: Make this into a generic definition of all `AbstractArray`?
+using NDTensors.NestedPermutedDimsArrays: NestedPermutedDimsArray
+function SparseArrayInterface.stored_indices(
+  a::NestedPermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:SparseArray}
+)
+  return Iterators.map(
+    I -> CartesianIndex(map(i -> I[i], perm(a))), stored_indices(parent(a))
+  )
+end
+
+# TODO: Make this into a generic definition of all `AbstractArray`?
+using NDTensors.NestedPermutedDimsArrays: NestedPermutedDimsArray
+using NDTensors.SparseArrayInterface: sparse_storage
+function SparseArrayInterface.sparse_storage(
+  a::NestedPermutedDimsArray{<:Any,<:Any,<:Any,<:Any,<:SparseArray}
+)
+  return sparse_storage(parent(a))
+end
+
 # Empty the storage, helps with efficiency in `map!` to drop
 # zeros.
 function SparseArrayInterface.dropall!(a::SparseArray)
diff --git a/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl b/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl
index 8ec5174463..0c44c25f6d 100644
--- a/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl
+++ b/NDTensors/src/lib/SparseArrayInterface/test/test_abstractsparsearray.jl
@@ -1,6 +1,7 @@
 @eval module $(gensym())
 using LinearAlgebra: dot, mul!, norm
 using NDTensors.SparseArrayInterface: SparseArrayInterface
+using NDTensors.NestedPermutedDimsArrays: NestedPermutedDimsArray
 include("SparseArrayInterfaceTestUtils/SparseArrayInterfaceTestUtils.jl")
 using .SparseArrayInterfaceTestUtils.AbstractSparseArrays: AbstractSparseArrays
 using .SparseArrayInterfaceTestUtils.SparseArrays: SparseArrays
@@ -224,6 +225,44 @@ using Test: @test, @testset
     end
   end
 
+  a = SparseArray{elt}(2, 3)
+  a[1, 2] = 12
+  b = PermutedDimsArray(a, (2, 1))
+  @test size(b) == (3, 2)
+  @test axes(b) == (1:3, 1:2)
+  @test SparseArrayInterface.sparse_storage(b) == elt[12]
+  @test SparseArrayInterface.stored_length(b) == 1
+  @test collect(SparseArrayInterface.stored_indices(b)) == [CartesianIndex(2, 1)]
+  @test !iszero(b)
+  @test !iszero(norm(b))
+  for I in eachindex(b)
+    if I == CartesianIndex(2, 1)
+      @test b[I] == 12
+    else
+      @test iszero(b[I])
+    end
+  end
+
+  a = SparseArray{Matrix{elt}}(
+    2, 3; zero=(a, I) -> (z = similar(eltype(a), 2, 3); fill!(z, false); z)
+  )
+  a[1, 2] = randn(elt, 2, 3)
+  b = NestedPermutedDimsArray(a, (2, 1))
+  @test size(b) == (3, 2)
+  @test axes(b) == (1:3, 1:2)
+  @test SparseArrayInterface.sparse_storage(b) == [a[1, 2]]
+  @test SparseArrayInterface.stored_length(b) == 1
+  @test collect(SparseArrayInterface.stored_indices(b)) == [CartesianIndex(2, 1)]
+  @test !iszero(b)
+  @test !iszero(norm(b))
+  for I in eachindex(b)
+    if I == CartesianIndex(2, 1)
+      @test b[I] == permutedims(a[1, 2], (2, 1))
+    else
+      @test iszero(b[I])
+    end
+  end
+
   a = SparseArray{elt}(2, 3)
   a[1, 2] = 12
   b = randn(elt, 2, 3)