diff --git a/ext/TensorKitGPUArraysExt.jl b/ext/TensorKitGPUArraysExt.jl
index 158890aa8..3176336b1 100644
--- a/ext/TensorKitGPUArraysExt.jl
+++ b/ext/TensorKitGPUArraysExt.jl
@@ -3,14 +3,18 @@ module TensorKitGPUArraysExt
 using GPUArrays
 using GPUArrays: @allowscalar
 using GPUArrays.KernelAbstractions: @kernel, @index, get_backend
-
+using Adapt
+using TensorKit.LRUCache: LRU
+using TensorKit.TupleTools
 using Strided: StridedViews
 using MatrixAlgebraKit, Adapt
 using TensorKit
+using TensorKit.TensorOperations: linearize, DefaultAllocator
 using TensorKit.Factorizations
 using TensorKit.Factorizations: AbstractAlgorithm
 using TensorKit: SectorDict, tensormaptype, scalar, similarstoragetype, AdjointTensorMap, scalartype, project_symmetric_and_check
-import TensorKit: randisometry, rand, randn, fill_braidingsubblock!
+using TensorKit: StridedSubblocks, UniqueTreeTransformer
+import TensorKit: randisometry, rand, randn, fill_braidingsubblock!, add_transform_kernel!
 
 function TensorKit.fill_braidingsubblock!(data::TD, val) where {T, TD <: Union{<:AnyGPUMatrix{T}, <:StridedViews.StridedView{T, 4, <:AnyGPUArray{T}}}}
     # COV_EXCL_START
@@ -121,5 +125,204 @@ function TensorKit.scalar(t::TensorMap{T, S, 0, 0, <:AnyGPUArray}) where {T, S}
     return isempty(inds) ? zero(scalartype(t)) : @allowscalar @inbounds t.data[only(inds)]
 end
 
+# Device-side tree transformers
+# -----------------------------
+# A `TreeTransformer` stores the mapping between subblock positions (plus recoupling
+# coefficients) and the `StridedStructure`s of the source and destination spaces.
+# We resolve the positions into sizes/strides/offsets and pack all the information on the
+# CPU side into dense vectors of numbers, plus some accounting information so we know how
+# to unpack in the kernel. Also, we can permute the source strides "in advance" on the CPU side.
+# We also precompute the strides of the subblock each kernel index will work on,
+# so that the GPU thread can recover the Cartesian coordinates it will need for input/ouput,
+# and a running `work_offsets` count of destination elements, so that a kernel can run one
+# thread per output element and recover which input that element belongs with.
+
+# Some possible TODO here:
+# - Try cuTILE as this is a classic tile programming problem
+# - Use shared memory to coalesce the reads
+# - Use a 2D grid for the Generic case
+
+const TreeStructure{N} = Tuple{NTuple{N, Int}, Int}
+
+"""
+    UniqueTransformerBlock{T, N}
+
+`isbits` descriptor for a subblock that is a *single* scaled permutation:
+an entry of a `UniqueTreeTransformer`.
+"""
+struct UniqueTransformerBlock{T, N}
+    coeff::T
+    sz::NTuple{N, Int}
+    dense_strides::NTuple{N, Int}
+    strides_dst::NTuple{N, Int}
+    offsets_dst::Int
+    permuted_strides_src::NTuple{N, Int}  # source strides, permuted by `p`
+    offsets_src::Int
+end
+
+# device-side simple struct that GPU kernels can use
+struct DeviceUniqueTreeTransformer{VB <: AbstractVector{<:UniqueTransformerBlock}, VO <: AbstractVector{Int}}
+    blocks::VB
+    work_offsets::VO
+    nwork::Int
+end
+
+# strides of a dense array of shape `sz`
+_dense_strides(size::Dims) = (1, Base.front(cumprod(size))...)
+
+# `permute(Vsrc, p) == Vdst` is enforced when the transformer is built, so the permuted
+# source shape always matches `sz_dst` and the two views share Cartesian inds.
+function _unique_block(
+        coeff::T, (size_dst, strides_dst, offsets_dst), (_, strides_src, offsets_src), p
+    ) where {T}
+    return UniqueTransformerBlock{T, length(size_dst)}(
+        coeff, size_dst, _dense_strides(size_dst), strides_dst, offsets_dst,
+        TupleTools.getindices(strides_src, p), offsets_src
+    )
+end
+
+function _work_offsets(work)
+    offsets = cumsum(work)
+    pushfirst!(offsets, 0)
+    total = pop!(offsets)
+    return offsets, total
+end
+
+function DeviceUniqueTreeTransformer(transformer::UniqueTreeTransformer{T, N}, p) where {T, N}
+    (; structure_dst, structure_src) = transformer
+    blocks = UniqueTransformerBlock{T, N}[
+        _unique_block(coeff, structure_dst[idst], structure_src[isrc], p)
+            for (coeff, idst, isrc) in transformer.data
+    ]
+    work_offsets, nwork = _work_offsets(prod(blk.sz) for blk in blocks)
+    return DeviceUniqueTreeTransformer(blocks, work_offsets, nwork)
+end
+
+"""
+    StorageAdaptor(proto)
+
+`Adapt` adaptor moving arrays onto the same device and array type as `proto`, preserving
+their element type. For `proto::CuVector{Float64}` and `array::Vector{Int}`, the call `adapt(typeof(proto), array)` would force-convert the element type `Int`
+to `Float64`, while `adapt(StoreAdaptor(proto), array)` does not.
+"""
+struct StorageAdaptor{A <: AbstractArray}
+    proto::A
+end
+function Adapt.adapt_storage(a::StorageAdaptor, x::AbstractArray)
+    dst = similar(a.proto, eltype(x), size(x))
+    isempty(x) && return dst
+    return copy!(dst, x)
+end
+
+function Adapt.adapt_structure(to, t::DeviceUniqueTreeTransformer)
+    return DeviceUniqueTreeTransformer(
+        Adapt.adapt(to, t.blocks), Adapt.adapt(to, t.work_offsets), t.nwork
+    )
+end
+
+# Copying a transformer to GPU is more expensive than running it, so we cache the device
+# copy in a global LRU cache, registered in `TensorKit.GLOBAL_CACHES` so that
+# `empty_globalcaches!` also frees the device memory. The key is:
+# - transformer which is an immutable struct. It's hashed and compared by the identity of
+#   its fields, which avoids walking every recoupling matrix on every lookup.
+#   Holding it in the key also keeps it alive, so its `objectid` cannot be
+#   reused by a different transformer while the entry is cached.
+# - the storage type
+# - `p`, which is baked into the permuted source strides.
+# TODO: should this live in the main package?
+const DEVICE_TRANSFORMER_CACHE = LRU{Any, Any}(; maxsize = TensorKit.DEFAULT_GLOBALCACHE_SIZE[])
+
+function __init__()
+    push!(TensorKit.GLOBAL_CACHES, :DEVICE_TRANSFORMER_CACHE => DEVICE_TRANSFORMER_CACHE)
+    return nothing
+end
+
+# We have this complicated setup because a naive `adapt` doesn't work.
+# Rather we copy everything to GPU-native arrays and have kernels that can work
+# with that.
+function device_transformer(proto::AbstractArray, transformer, p)
+    key = (transformer, typeof(proto), p)
+    return get!(DEVICE_TRANSFORMER_CACHE, key) do
+        # be careful about the lifetime of these, since they live in a global cache and
+        # thus persist beyond the call
+        GPUArrays.@uncached Adapt.adapt(
+            StorageAdaptor(proto), _device_transformer(transformer, p)
+        )
+    end
+end
+
+_device_transformer(t::UniqueTreeTransformer, p) = DeviceUniqueTreeTransformer(t, p)
+
+# COV_EXCL_START
+# kernels are not reachable by coverage
+
+# largest `i` with `offsets[i] <= w`. This corresponds to the
+# block which  this kernel thread will work on. Since this is
+# used inside a GPU kernel, searchsortedlast/searchsortedfirst
+# won't work.
+@inline function _searchblock(offsets, w)
+    lo, hi = 1, length(offsets)
+    while lo < hi
+        mid = (lo + hi + 1) >>> 1
+        if @inbounds offsets[mid] <= w
+            lo = mid
+        else
+            hi = mid - 1
+        end
+    end
+    return lo
+end
+
+# Cartesian coordinates of the `w`-th (0-based) entry of a dense subblock of shape `sz`.
+@inline function _coordinates(w, size::NTuple{N, Int}, dense_strides::NTuple{N, Int}) where {N}
+    return ntuple(n -> (w ÷ dense_strides[n]) % size[n], Val(N))
+end
+
+# finds the overall linear index in the output and input arrays corresponding to the **sublock**
+# coordinates currently being worked on
+@inline function _linear_index(coords::NTuple{N, Int}, strides::NTuple{N, Int}, offset) where {N}
+    return offset + sum(ntuple(n -> coords[n] * strides[n], Val(N))) + 1
+end
+
+# One thread per destination element in `data_dst`. `op` is `identity` or `conj`, and is
+# applied to the source data only (not to the coefficients).
+@kernel function unique_batched_permute_kernel!(
+        data_dst, data_src, op, blocks, work_offsets, α, β, nwork, ::Val{N}
+    ) where {N}
+    w = @index(Global, Linear) - 1
+    if w < nwork
+        b = _searchblock(work_offsets, w)
+        blk = @inbounds blocks[b]
+        coords = _coordinates(w - (@inbounds work_offsets[b]), blk.sz, blk.dense_strides)
+        i_dst = _linear_index(coords, blk.strides_dst, blk.offsets_dst)
+        i_src = _linear_index(coords, blk.permuted_strides_src, blk.offsets_src)
+        @inbounds data_dst[i_dst] = α * blk.coeff * op(data_src[i_src]) + β * data_dst[i_dst]
+    end
+end
+
+# COV_EXCL_STOP
+
+function _launch_unique!(data_dst, data_src, op, transformer, α, β, ::Val{N}) where {N}
+    nwork = transformer.nwork
+    nwork == 0 && return nothing
+    unique_batched_permute_kernel!(get_backend(data_dst))(
+        data_dst, data_src, op, transformer.blocks, transformer.work_offsets, α, β, nwork,
+        Val(N); ndrange = nwork
+    )
+    return nothing
+end
+
+const GPUStridedSubblocks = StridedSubblocks{<:AnyGPUArray}
+
+function TensorKit.add_transform_kernel!(
+        dst::GPUStridedSubblocks, src::GPUStridedSubblocks, p, conjsrc::Bool,
+        transformer::UniqueTreeTransformer{T, N}, α, β, backend, allocator, ntasks::Int
+    ) where {T, N}
+    # GPU-side object to hold the treetransformer information
+    device = device_transformer(dst.data, transformer, linearize(p))
+    op = conjsrc ? conj : identity
+    _launch_unique!(dst.data, src.data, op, device, α, β, Val(N))
+    return nothing
+end
 
 end