diff --git a/Project.toml b/Project.toml
index daa62a5e42..db6403c628 100644
--- a/Project.toml
+++ b/Project.toml
@@ -41,11 +41,13 @@ demumble_jll = "1e29f10c-031c-5a83-9565-69cddfc27673"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+SparseMatricesCSR = "a0a7dd2c-ebf4-11e9-1f05-cf50bc540ca1"
 
 [extensions]
 ChainRulesCoreExt = "ChainRulesCore"
 EnzymeCoreExt = "EnzymeCore"
 SpecialFunctionsExt = "SpecialFunctions"
+SparseMatricesCSRExt = "SparseMatricesCSR"
 
 [compat]
 AbstractFFTs = "0.4, 0.5, 1.0"
@@ -80,6 +82,7 @@ RandomNumbers = "1.5.3"
 Reexport = "0.2, 1.0"
 Requires = "0.5, 1.0"
 SparseArrays = "1"
+SparseMatricesCSR = "0.6.9"
 SpecialFunctions = "1.3, 2"
 StaticArrays = "1"
 Statistics = "1"
@@ -90,3 +93,4 @@ julia = "1.10"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+SparseMatricesCSR = "a0a7dd2c-ebf4-11e9-1f05-cf50bc540ca1"
diff --git a/ext/SparseMatricesCSRExt.jl b/ext/SparseMatricesCSRExt.jl
new file mode 100644
index 0000000000..7ffe884014
--- /dev/null
+++ b/ext/SparseMatricesCSRExt.jl
@@ -0,0 +1,32 @@
+module SparseMatricesCSRExt
+
+using CUDA
+import CUDA.CUSPARSE:
+    CuSparseMatrixCSR, CuSparseMatrixCSC, CuSparseMatrixCOO, CuSparseMatrixBSR,
+    SparseMatrixCSC
+using SparseMatricesCSR
+import SparseMatricesCSR: SparseMatrixCSR
+import Adapt
+
+# CPU → GPU
+CUSPARSE.CuSparseMatrixCSR{T}(Mat::SparseMatrixCSR) where {T} =
+    CUSPARSE.CuSparseMatrixCSR{T}(
+    CuVector{Cint}(Mat.rowptr), CuVector{Cint}(Mat.colval),
+    CuVector{T}(Mat.nzval), size(Mat)
+)
+CUSPARSE.CuSparseMatrixCSC{T}(Mat::SparseMatrixCSR) where {T} = CuSparseMatrixCSC(CuSparseMatrixCSR{T}(Mat))
+CUSPARSE.CuSparseMatrixCOO{T}(Mat::SparseMatrixCSR) where {T} = CuSparseMatrixCOO(CuSparseMatrixCSR{T}(Mat))
+CUSPARSE.CuSparseMatrixBSR{T}(Mat::SparseMatrixCSR, blockdim) where {T} = CuSparseMatrixBSR(CuSparseMatrixCSR{T}(Mat), blockdim)
+
+# GPU → CPU
+SparseMatricesCSR.SparseMatrixCSR(A::CUSPARSE.CuSparseMatrixCSR) = SparseMatrixCSR{1}(size(A)..., Array(A.rowPtr), Array(A.colVal), Array(A.nzVal))
+SparseMatricesCSR.SparseMatrixCSR(A::CUSPARSE.CuSparseMatrixCOO) = SparseMatrixCSR(CuSparseMatrixCSR(A))
+SparseMatricesCSR.SparseMatrixCSR(A::CUSPARSE.CuSparseMatrixCSC) = SparseMatrixCSR(CuSparseMatrixCSR(A))
+SparseMatricesCSR.SparseMatrixCSR(A::CUSPARSE.CuSparseMatrixBSR) = SparseMatrixCSR(CuSparseMatrixCSR(A))
+
+# Adapt
+Adapt.adapt_storage(::Type{CuArray}, xs::SparseMatrixCSR) = CUSPARSE.CuSparseMatrixCSR(xs)
+Adapt.adapt_storage(::Type{CuArray{T}}, xs::SparseMatrixCSR) where {T} = CUSPARSE.CuSparseMatrixCSR{T}(xs)
+Adapt.adapt_storage(::Type{Array}, mat::CUSPARSE.CuSparseMatrixCSR) = SparseMatrixCSR(mat)
+
+end
diff --git a/test/extensions/sparse_matrices_csr.jl b/test/extensions/sparse_matrices_csr.jl
new file mode 100644
index 0000000000..032a7ec8df
--- /dev/null
+++ b/test/extensions/sparse_matrices_csr.jl
@@ -0,0 +1,30 @@
+using SparseMatricesCSR
+using SparseArrays
+using CUDA
+using CUDA.CUSPARSE
+using Test
+
+@testset "SparseMatricesCSRExt" begin
+
+    for (n, bd, p) in [(100, 5, 0.02), (5, 1, 0.8), (4, 2, 0.5)]
+        v"12.0" <= CUSPARSE.version() < v"12.1" && n == 4 && continue
+        @testset "conversions between CuSparseMatrices (n, bd, p) = ($n, $bd, $p)" begin
+            _A = sprand(n, n, p)
+            A = SparseMatrixCSR(_A)
+            blockdim = bd
+            for CuSparseMatrixType1 in (CuSparseMatrixCSC, CuSparseMatrixCSR, CuSparseMatrixCOO, CuSparseMatrixBSR)
+                dA1 = CuSparseMatrixType1 == CuSparseMatrixBSR ? CuSparseMatrixType1(A, blockdim) : CuSparseMatrixType1(A)
+                @testset "conversion $CuSparseMatrixType1 --> SparseMatrixCSR" begin
+                    @test SparseMatrixCSR(dA1) ≈ A
+                end
+                for CuSparseMatrixType2 in (CuSparseMatrixCSC, CuSparseMatrixCSR, CuSparseMatrixCOO, CuSparseMatrixBSR)
+                    CuSparseMatrixType1 == CuSparseMatrixType2 && continue
+                    dA2 = CuSparseMatrixType2 == CuSparseMatrixBSR ? CuSparseMatrixType2(dA1, blockdim) : CuSparseMatrixType2(dA1)
+                    @testset "conversion $CuSparseMatrixType1 --> $CuSparseMatrixType2" begin
+                        @test collect(dA1) ≈ collect(dA2)
+                    end
+                end
+            end
+        end
+    end
+end