diff --git a/include/xgboost/data.h b/include/xgboost/data.h
index 472ca43b3c3a..eae2f612bc45 100644
--- a/include/xgboost/data.h
+++ b/include/xgboost/data.h
@@ -185,10 +185,10 @@ class MetaInfo {
     return data_split_mode == DataSplitMode::kRow;
   }
 
-  /*! \brief Whether the data is split column-wise. */
-  bool IsColumnSplit() const {
-    return data_split_mode == DataSplitMode::kCol;
-  }
+  /** @brief Whether the data is split column-wise. */
+  bool IsColumnSplit() const { return data_split_mode == DataSplitMode::kCol; }
+  /** @brief Whether this is a learning to rank data. */
+  bool IsRanking() const { return !group_ptr_.empty(); }
 
   /*!
    * \brief A convenient method to check if we are doing vertical federated learning, which requires
@@ -249,7 +249,7 @@ struct BatchParam {
   /**
    * \brief Hessian, used for sketching with future approx implementation.
    */
-  common::Span<float> hess;
+  common::Span<float const> hess;
   /**
    * \brief Whether should we force DMatrix to regenerate the batch.  Only used for
    *        GHistIndex.
@@ -279,7 +279,7 @@ struct BatchParam {
    *   Get batch with sketch weighted by hessian.  The batch will be regenerated if the
    *   span is changed, so caller should keep the span for each iteration.
    */
-  BatchParam(bst_bin_t max_bin, common::Span<float> hessian, bool regenerate)
+  BatchParam(bst_bin_t max_bin, common::Span<float const> hessian, bool regenerate)
       : max_bin{max_bin}, hess{hessian}, regen{regenerate} {}
 
   [[nodiscard]] bool ParamNotEqual(BatchParam const& other) const {
diff --git a/include/xgboost/host_device_vector.h b/include/xgboost/host_device_vector.h
index b9fb151047c6..b221d72067d1 100644
--- a/include/xgboost/host_device_vector.h
+++ b/include/xgboost/host_device_vector.h
@@ -49,11 +49,12 @@
 #ifndef XGBOOST_HOST_DEVICE_VECTOR_H_
 #define XGBOOST_HOST_DEVICE_VECTOR_H_
 
+#include <xgboost/context.h>  // for DeviceOrd
+#include <xgboost/span.h>     // for Span
+
 #include <initializer_list>
-#include <vector>
 #include <type_traits>
-
-#include "span.h"
+#include <vector>
 
 namespace xgboost {
 
@@ -133,6 +134,7 @@ class HostDeviceVector {
   GPUAccess DeviceAccess() const;
 
   void SetDevice(int device) const;
+  void SetDevice(DeviceOrd device) const;
 
   void Resize(size_t new_size, T v = T());
 
diff --git a/src/common/hist_util.cc b/src/common/hist_util.cc
index c9b50792d073..4e12ebc4cc85 100644
--- a/src/common/hist_util.cc
+++ b/src/common/hist_util.cc
@@ -8,12 +8,12 @@
 
 #include <vector>
 
-#include "../common/common.h"
-#include "column_matrix.h"
+#include "../data/adapter.h"         // for SparsePageAdapterBatch
+#include "../data/gradient_index.h"  // for GHistIndexMatrix
 #include "quantile.h"
 #include "xgboost/base.h"
-#include "xgboost/context.h"  // Context
-#include "xgboost/data.h"     // SparsePage, SortedCSCPage
+#include "xgboost/context.h"  // for Context
+#include "xgboost/data.h"     // for SparsePage, SortedCSCPage
 
 #if defined(XGBOOST_MM_PREFETCH_PRESENT)
   #include <xmmintrin.h>
@@ -32,7 +32,7 @@ HistogramCuts::HistogramCuts() {
 }
 
 HistogramCuts SketchOnDMatrix(Context const *ctx, DMatrix *m, bst_bin_t max_bins, bool use_sorted,
-                              Span<float> const hessian) {
+                              Span<float const> hessian) {
   HistogramCuts out;
   auto const &info = m->Info();
   auto n_threads = ctx->Threads();
diff --git a/src/common/hist_util.cu b/src/common/hist_util.cu
index eabdb86de278..2dfba72158bb 100644
--- a/src/common/hist_util.cu
+++ b/src/common/hist_util.cu
@@ -19,14 +19,13 @@
 #include <vector>
 
 #include "categorical.h"
+#include "cuda_context.cuh"  // for CUDAContext
 #include "device_helpers.cuh"
 #include "hist_util.cuh"
 #include "hist_util.h"
-#include "math.h"  // NOLINT
 #include "quantile.h"
 #include "xgboost/host_device_vector.h"
 
-
 namespace xgboost::common {
 constexpr float SketchContainer::kFactor;
 
@@ -109,22 +108,19 @@ size_t SketchBatchNumElements(size_t sketch_batch_num_elements, bst_row_t num_ro
   return std::min(sketch_batch_num_elements, kIntMax);
 }
 
-void SortByWeight(dh::device_vector<float>* weights,
-                  dh::device_vector<Entry>* sorted_entries) {
+void SortByWeight(dh::device_vector<float>* weights, dh::device_vector<Entry>* sorted_entries) {
   // Sort both entries and wegihts.
   dh::XGBDeviceAllocator<char> alloc;
-  thrust::sort_by_key(thrust::cuda::par(alloc), sorted_entries->begin(),
-                      sorted_entries->end(), weights->begin(),
-                      detail::EntryCompareOp());
+  CHECK_EQ(weights->size(), sorted_entries->size());
+  thrust::sort_by_key(thrust::cuda::par(alloc), sorted_entries->begin(), sorted_entries->end(),
+                      weights->begin(), detail::EntryCompareOp());
 
   // Scan weights
   dh::XGBCachingDeviceAllocator<char> caching;
-  thrust::inclusive_scan_by_key(thrust::cuda::par(caching),
-                                sorted_entries->begin(), sorted_entries->end(),
-                                weights->begin(), weights->begin(),
-                                [=] __device__(const Entry& a, const Entry& b) {
-                                  return a.index == b.index;
-                                });
+  thrust::inclusive_scan_by_key(
+      thrust::cuda::par(caching), sorted_entries->begin(), sorted_entries->end(), weights->begin(),
+      weights->begin(),
+      [=] __device__(const Entry& a, const Entry& b) { return a.index == b.index; });
 }
 
 void RemoveDuplicatedCategories(int32_t device, MetaInfo const& info, Span<bst_row_t> d_cuts_ptr,
@@ -200,159 +196,170 @@ void RemoveDuplicatedCategories(int32_t device, MetaInfo const& info, Span<bst_r
 }
 }  // namespace detail
 
-void ProcessBatch(int device, MetaInfo const &info, const SparsePage &page,
-                  size_t begin, size_t end, SketchContainer *sketch_container,
-                  int num_cuts_per_feature, size_t num_columns) {
-  dh::XGBCachingDeviceAllocator<char> alloc;
+void ProcessWeightedBatch(Context const* ctx, const SparsePage& page, MetaInfo const& info,
+                          std::size_t begin, std::size_t end,
+                          SketchContainer* sketch_container,  // <- output sketch
+                          int num_cuts_per_feature, common::Span<float const> sample_weight) {
   dh::device_vector<Entry> sorted_entries;
   if (page.data.DeviceCanRead()) {
-    const auto& device_data = page.data.ConstDevicePointer();
-    sorted_entries = dh::device_vector<Entry>(device_data + begin, device_data + end);
+    // direct copy if data is already on device
+    auto const& d_data = page.data.ConstDevicePointer();
+    sorted_entries = dh::device_vector<Entry>(d_data + begin, d_data + end);
+  } else {
+    const auto& h_data = page.data.ConstHostVector();
+    sorted_entries = dh::device_vector<Entry>(h_data.begin() + begin, h_data.begin() + end);
+  }
+
+  bst_row_t base_rowid = page.base_rowid;
+
+  dh::device_vector<float> entry_weight;
+  auto cuctx = ctx->CUDACtx();
+  if (!sample_weight.empty()) {
+    // Expand sample weight into entry weight.
+    CHECK_EQ(sample_weight.size(), info.num_row_);
+    entry_weight.resize(sorted_entries.size());
+    auto d_temp_weight = dh::ToSpan(entry_weight);
+    page.offset.SetDevice(ctx->Device());
+    auto row_ptrs = page.offset.ConstDeviceSpan();
+    thrust::for_each_n(cuctx->CTP(), thrust::make_counting_iterator(0ul), entry_weight.size(),
+                       [=] __device__(std::size_t idx) {
+                         std::size_t element_idx = idx + begin;
+                         std::size_t ridx = dh::SegmentId(row_ptrs, element_idx);
+                         d_temp_weight[idx] = sample_weight[ridx + base_rowid];
+                       });
+    detail::SortByWeight(&entry_weight, &sorted_entries);
   } else {
-    const auto& host_data = page.data.ConstHostVector();
-    sorted_entries = dh::device_vector<Entry>(host_data.begin() + begin,
-                                              host_data.begin() + end);
+    thrust::sort(cuctx->CTP(), sorted_entries.begin(), sorted_entries.end(),
+                 detail::EntryCompareOp());
   }
-  thrust::sort(thrust::cuda::par(alloc), sorted_entries.begin(),
-               sorted_entries.end(), detail::EntryCompareOp());
 
   HostDeviceVector<SketchContainer::OffsetT> cuts_ptr;
   dh::caching_device_vector<size_t> column_sizes_scan;
   data::IsValidFunctor dummy_is_valid(std::numeric_limits<float>::quiet_NaN());
   auto batch_it = dh::MakeTransformIterator<data::COOTuple>(
-      sorted_entries.data().get(),
-      [] __device__(Entry const &e) -> data::COOTuple {
-        return {0, e.index, e.fvalue};  // row_idx is not needed for scanning column size.
+      sorted_entries.data().get(), [] __device__(Entry const& e) -> data::COOTuple {
+        return {0, e.index, e.fvalue};  // row_idx is not needed for scaning column size.
       });
-  detail::GetColumnSizesScan(device, num_columns, num_cuts_per_feature,
+  detail::GetColumnSizesScan(ctx->Ordinal(), info.num_col_, num_cuts_per_feature,
                              IterSpan{batch_it, sorted_entries.size()}, dummy_is_valid, &cuts_ptr,
                              &column_sizes_scan);
   auto d_cuts_ptr = cuts_ptr.DeviceSpan();
-
   if (sketch_container->HasCategorical()) {
-    detail::RemoveDuplicatedCategories(device, info, d_cuts_ptr, &sorted_entries, nullptr,
+    auto p_weight = entry_weight.empty() ? nullptr : &entry_weight;
+    detail::RemoveDuplicatedCategories(ctx->Ordinal(), info, d_cuts_ptr, &sorted_entries, p_weight,
                                        &column_sizes_scan);
   }
 
   auto const& h_cuts_ptr = cuts_ptr.ConstHostVector();
   CHECK_EQ(d_cuts_ptr.size(), column_sizes_scan.size());
 
-  // add cuts into sketches
-  sketch_container->Push(dh::ToSpan(sorted_entries), dh::ToSpan(column_sizes_scan),
-                         d_cuts_ptr, h_cuts_ptr.back());
+  // Add cuts into sketches
+  sketch_container->Push(dh::ToSpan(sorted_entries), dh::ToSpan(column_sizes_scan), d_cuts_ptr,
+                         h_cuts_ptr.back(), dh::ToSpan(entry_weight));
+
   sorted_entries.clear();
   sorted_entries.shrink_to_fit();
   CHECK_EQ(sorted_entries.capacity(), 0);
   CHECK_NE(cuts_ptr.Size(), 0);
 }
 
-void ProcessWeightedBatch(int device, const SparsePage& page,
-                          MetaInfo const& info, size_t begin, size_t end,
-                          SketchContainer* sketch_container, int num_cuts_per_feature,
-                          size_t num_columns,
-                          bool is_ranking, Span<bst_group_t const> d_group_ptr) {
-  auto weights = info.weights_.ConstDeviceSpan();
-
-  dh::XGBCachingDeviceAllocator<char> alloc;
-  const auto& host_data = page.data.ConstHostVector();
-  dh::device_vector<Entry> sorted_entries(host_data.begin() + begin,
-                                          host_data.begin() + end);
-
-  // Binary search to assign weights to each element
-  dh::device_vector<float> temp_weights(sorted_entries.size());
-  auto d_temp_weights = temp_weights.data().get();
-  page.offset.SetDevice(device);
-  auto row_ptrs = page.offset.ConstDeviceSpan();
-  size_t base_rowid = page.base_rowid;
-  if (is_ranking) {
-    CHECK_GE(d_group_ptr.size(), 2)
-        << "Must have at least 1 group for ranking.";
-    CHECK_EQ(weights.size(), d_group_ptr.size() - 1)
-        << "Weight size should equal to number of groups.";
-    dh::LaunchN(temp_weights.size(), [=] __device__(size_t idx) {
-        size_t element_idx = idx + begin;
-        size_t ridx = dh::SegmentId(row_ptrs, element_idx);
-        bst_group_t group_idx = dh::SegmentId(d_group_ptr, ridx + base_rowid);
-        d_temp_weights[idx] = weights[group_idx];
-      });
-  } else {
-    dh::LaunchN(temp_weights.size(), [=] __device__(size_t idx) {
-        size_t element_idx = idx + begin;
-        size_t ridx = dh::SegmentId(row_ptrs, element_idx);
-        d_temp_weights[idx] = weights[ridx + base_rowid];
-      });
+// Unify group weight, Hessian, and sample weight into sample weight.
+[[nodiscard]] Span<float const> UnifyWeight(CUDAContext const* cuctx, MetaInfo const& info,
+                                            common::Span<float const> hessian,
+                                            HostDeviceVector<float>* p_out_weight) {
+  if (hessian.empty()) {
+    if (info.IsRanking() && !info.weights_.Empty()) {
+      common::Span<float const> group_weight = info.weights_.ConstDeviceSpan();
+      dh::device_vector<bst_group_t> group_ptr(info.group_ptr_);
+      auto d_group_ptr = dh::ToSpan(group_ptr);
+      CHECK_GE(d_group_ptr.size(), 2) << "Must have at least 1 group for ranking.";
+      auto d_weight = info.weights_.ConstDeviceSpan();
+      CHECK_EQ(d_weight.size(), d_group_ptr.size() - 1)
+          << "Weight size should equal to number of groups.";
+      p_out_weight->Resize(info.num_row_);
+      auto d_weight_out = p_out_weight->DeviceSpan();
+
+      thrust::for_each_n(cuctx->CTP(), thrust::make_counting_iterator(0ul), d_weight_out.size(),
+                         [=] XGBOOST_DEVICE(std::size_t i) {
+                           auto gidx = dh::SegmentId(d_group_ptr, i);
+                           d_weight_out[i] = d_weight[gidx];
+                         });
+      return p_out_weight->ConstDeviceSpan();
+    } else {
+      return info.weights_.ConstDeviceSpan();
+    }
   }
-  detail::SortByWeight(&temp_weights, &sorted_entries);
 
-  HostDeviceVector<SketchContainer::OffsetT> cuts_ptr;
-  dh::caching_device_vector<size_t> column_sizes_scan;
-  data::IsValidFunctor dummy_is_valid(std::numeric_limits<float>::quiet_NaN());
-  auto batch_it = dh::MakeTransformIterator<data::COOTuple>(
-      sorted_entries.data().get(),
-      [] __device__(Entry const &e) -> data::COOTuple {
-        return {0, e.index, e.fvalue};  // row_idx is not needed for scaning column size.
-      });
-  detail::GetColumnSizesScan(device, num_columns, num_cuts_per_feature,
-                             IterSpan{batch_it, sorted_entries.size()}, dummy_is_valid, &cuts_ptr,
-                             &column_sizes_scan);
-  auto d_cuts_ptr = cuts_ptr.DeviceSpan();
-  if (sketch_container->HasCategorical()) {
-    detail::RemoveDuplicatedCategories(device, info, d_cuts_ptr, &sorted_entries, &temp_weights,
-                                       &column_sizes_scan);
+  // sketch with hessian as weight
+  p_out_weight->Resize(info.num_row_);
+  auto d_weight_out = p_out_weight->DeviceSpan();
+  if (!info.weights_.Empty()) {
+    // merge sample weight with hessian
+    auto d_weight = info.weights_.ConstDeviceSpan();
+    if (info.IsRanking()) {
+      dh::device_vector<bst_group_t> group_ptr(info.group_ptr_);
+      CHECK_EQ(hessian.size(), d_weight_out.size());
+      auto d_group_ptr = dh::ToSpan(group_ptr);
+      CHECK_GE(d_group_ptr.size(), 2) << "Must have at least 1 group for ranking.";
+      CHECK_EQ(d_weight.size(), d_group_ptr.size() - 1)
+          << "Weight size should equal to number of groups.";
+      thrust::for_each_n(cuctx->CTP(), thrust::make_counting_iterator(0ul), hessian.size(),
+                         [=] XGBOOST_DEVICE(std::size_t i) {
+                           d_weight_out[i] = d_weight[dh::SegmentId(d_group_ptr, i)] * hessian(i);
+                         });
+    } else {
+      CHECK_EQ(hessian.size(), info.num_row_);
+      CHECK_EQ(hessian.size(), d_weight.size());
+      CHECK_EQ(hessian.size(), d_weight_out.size());
+      thrust::for_each_n(
+          cuctx->CTP(), thrust::make_counting_iterator(0ul), hessian.size(),
+          [=] XGBOOST_DEVICE(std::size_t i) { d_weight_out[i] = d_weight[i] * hessian(i); });
+    }
+  } else {
+    // copy hessian as weight
+    CHECK_EQ(d_weight_out.size(), hessian.size());
+    dh::safe_cuda(cudaMemcpyAsync(d_weight_out.data(), hessian.data(), hessian.size_bytes(),
+                                  cudaMemcpyDefault));
   }
+  return d_weight_out;
+}
 
-  auto const& h_cuts_ptr = cuts_ptr.ConstHostVector();
+HistogramCuts DeviceSketchWithHessian(Context const* ctx, DMatrix* p_fmat, bst_bin_t max_bin,
+                                      Span<float const> hessian,
+                                      std::size_t sketch_batch_num_elements) {
+  auto const& info = p_fmat->Info();
+  bool has_weight = !info.weights_.Empty();
+  info.feature_types.SetDevice(ctx->Device());
 
-  // Extract cuts
-  sketch_container->Push(dh::ToSpan(sorted_entries),
-                         dh::ToSpan(column_sizes_scan), d_cuts_ptr,
-                         h_cuts_ptr.back(), dh::ToSpan(temp_weights));
-  sorted_entries.clear();
-  sorted_entries.shrink_to_fit();
-}
+  HostDeviceVector<float> weight;
+  weight.SetDevice(ctx->Device());
 
-HistogramCuts DeviceSketch(int device, DMatrix* dmat, int max_bins,
-                           size_t sketch_batch_num_elements) {
-  dmat->Info().feature_types.SetDevice(device);
-  dmat->Info().feature_types.ConstDevicePointer();  // pull to device early
   // Configure batch size based on available memory
-  bool has_weights = dmat->Info().weights_.Size() > 0;
-  size_t num_cuts_per_feature =
-      detail::RequiredSampleCutsPerColumn(max_bins, dmat->Info().num_row_);
+  std::size_t num_cuts_per_feature = detail::RequiredSampleCutsPerColumn(max_bin, info.num_row_);
   sketch_batch_num_elements = detail::SketchBatchNumElements(
-      sketch_batch_num_elements,
-      dmat->Info().num_row_,
-      dmat->Info().num_col_,
-      dmat->Info().num_nonzero_,
-      device, num_cuts_per_feature, has_weights);
+      sketch_batch_num_elements, info.num_row_, info.num_col_, info.num_nonzero_, ctx->Ordinal(),
+      num_cuts_per_feature, has_weight);
+
+  CUDAContext const* cuctx = ctx->CUDACtx();
+
+  info.weights_.SetDevice(ctx->Device());
+  auto d_weight = UnifyWeight(cuctx, info, hessian, &weight);
 
   HistogramCuts cuts;
-  SketchContainer sketch_container(dmat->Info().feature_types, max_bins, dmat->Info().num_col_,
-                                   dmat->Info().num_row_, device);
-
-  dmat->Info().weights_.SetDevice(device);
-  for (const auto& batch : dmat->GetBatches<SparsePage>()) {
-    size_t batch_nnz = batch.data.Size();
-    auto const& info = dmat->Info();
-    for (auto begin = 0ull; begin < batch_nnz; begin += sketch_batch_num_elements) {
-      size_t end = std::min(batch_nnz, static_cast<std::size_t>(begin + sketch_batch_num_elements));
-      if (has_weights) {
-        bool is_ranking = HostSketchContainer::UseGroup(dmat->Info());
-        dh::caching_device_vector<uint32_t> groups(info.group_ptr_.cbegin(),
-                                                   info.group_ptr_.cend());
-        ProcessWeightedBatch(
-            device, batch, dmat->Info(), begin, end,
-            &sketch_container,
-            num_cuts_per_feature,
-            dmat->Info().num_col_,
-            is_ranking, dh::ToSpan(groups));
-      } else {
-        ProcessBatch(device, dmat->Info(), batch, begin, end, &sketch_container,
-                     num_cuts_per_feature, dmat->Info().num_col_);
-      }
+  SketchContainer sketch_container(info.feature_types, max_bin, info.num_col_, info.num_row_,
+                                   ctx->Ordinal());
+  CHECK_EQ(has_weight || !hessian.empty(), !d_weight.empty());
+  for (const auto& page : p_fmat->GetBatches<SparsePage>()) {
+    std::size_t page_nnz = page.data.Size();
+    for (auto begin = 0ull; begin < page_nnz; begin += sketch_batch_num_elements) {
+      std::size_t end =
+          std::min(page_nnz, static_cast<std::size_t>(begin + sketch_batch_num_elements));
+      ProcessWeightedBatch(ctx, page, info, begin, end, &sketch_container, num_cuts_per_feature,
+                           d_weight);
     }
   }
-  sketch_container.MakeCuts(&cuts, dmat->Info().IsColumnSplit());
+
+  sketch_container.MakeCuts(&cuts, p_fmat->Info().IsColumnSplit());
   return cuts;
 }
 }  // namespace xgboost::common
diff --git a/src/common/hist_util.cuh b/src/common/hist_util.cuh
index 0dcdad64dbc1..f13f01b3e9ed 100644
--- a/src/common/hist_util.cuh
+++ b/src/common/hist_util.cuh
@@ -11,14 +11,13 @@
 
 #include <cstddef>  // for size_t
 
-#include "../data/device_adapter.cuh"
+#include "../data/adapter.h"  // for IsValidFunctor
 #include "device_helpers.cuh"
 #include "hist_util.h"
 #include "quantile.cuh"
-#include "timer.h"
+#include "xgboost/span.h"  // for IterSpan
 
-namespace xgboost {
-namespace common {
+namespace xgboost::common {
 namespace cuda {
 /**
  * copy and paste of the host version, we can't make it a __host__ __device__ function as
@@ -246,10 +245,35 @@ void RemoveDuplicatedCategories(int32_t device, MetaInfo const& info, Span<bst_r
                                 dh::caching_device_vector<size_t>* p_column_sizes_scan);
 }  // namespace detail
 
-// Compute sketch on DMatrix.
-// sketch_batch_num_elements 0 means autodetect. Only modify this for testing.
-HistogramCuts DeviceSketch(int device, DMatrix* dmat, int max_bins,
-                           size_t sketch_batch_num_elements = 0);
+/**
+ * @brief Compute sketch on DMatrix with GPU and Hessian as weight.
+ *
+ * @param ctx     Runtime context
+ * @param p_fmat  Training feature matrix
+ * @param max_bin Maximum number of bins for each feature
+ * @param hessian Hessian vector.
+ * @param sketch_batch_num_elements 0 means autodetect. Only modify this for testing.
+ *
+ * @return Quantile cuts
+ */
+HistogramCuts DeviceSketchWithHessian(Context const* ctx, DMatrix* p_fmat, bst_bin_t max_bin,
+                                      Span<float const> hessian,
+                                      std::size_t sketch_batch_num_elements = 0);
+
+/**
+ * @brief Compute sketch on DMatrix with GPU.
+ *
+ * @param ctx     Runtime context
+ * @param p_fmat  Training feature matrix
+ * @param max_bin Maximum number of bins for each feature
+ * @param sketch_batch_num_elements 0 means autodetect. Only modify this for testing.
+ *
+ * @return Quantile cuts
+ */
+inline HistogramCuts DeviceSketch(Context const* ctx, DMatrix* p_fmat, bst_bin_t max_bin,
+                                  std::size_t sketch_batch_num_elements = 0) {
+  return DeviceSketchWithHessian(ctx, p_fmat, max_bin, {}, sketch_batch_num_elements);
+}
 
 template <typename AdapterBatch>
 void ProcessSlidingWindow(AdapterBatch const &batch, MetaInfo const &info,
@@ -417,7 +441,5 @@ void AdapterDeviceSketch(Batch batch, int num_bins,
     }
   }
 }
-}      // namespace common
-}      // namespace xgboost
-
+}  // namespace xgboost::common
 #endif  // COMMON_HIST_UTIL_CUH_
diff --git a/src/common/hist_util.h b/src/common/hist_util.h
index 2781da8e0cff..18f208467a56 100644
--- a/src/common/hist_util.h
+++ b/src/common/hist_util.h
@@ -174,7 +174,7 @@ class HistogramCuts {
  *                   but consumes more memory.
  */
 HistogramCuts SketchOnDMatrix(Context const* ctx, DMatrix* m, bst_bin_t max_bins,
-                              bool use_sorted = false, Span<float> const hessian = {});
+                              bool use_sorted = false, Span<float const> hessian = {});
 
 enum BinTypeSize : uint8_t {
   kUint8BinsTypeSize = 1,
diff --git a/src/common/host_device_vector.cc b/src/common/host_device_vector.cc
index 55c0ecf202f8..175a5cbf1b10 100644
--- a/src/common/host_device_vector.cc
+++ b/src/common/host_device_vector.cc
@@ -168,6 +168,9 @@ bool HostDeviceVector<T>::DeviceCanWrite() const {
 template <typename T>
 void HostDeviceVector<T>::SetDevice(int) const {}
 
+template <typename T>
+void HostDeviceVector<T>::SetDevice(DeviceOrd) const {}
+
 // explicit instantiations are required, as HostDeviceVector isn't header-only
 template class HostDeviceVector<bst_float>;
 template class HostDeviceVector<double>;
diff --git a/src/common/host_device_vector.cu b/src/common/host_device_vector.cu
index 1fa9a3b2200c..7acb6719ba91 100644
--- a/src/common/host_device_vector.cu
+++ b/src/common/host_device_vector.cu
@@ -394,6 +394,11 @@ void HostDeviceVector<T>::SetDevice(int device) const {
   impl_->SetDevice(device);
 }
 
+template <typename T>
+void HostDeviceVector<T>::SetDevice(DeviceOrd device) const {
+  impl_->SetDevice(device.ordinal);
+}
+
 template <typename T>
 void HostDeviceVector<T>::Resize(size_t new_size, T v) {
   impl_->Resize(new_size, v);
diff --git a/src/data/ellpack_page.cu b/src/data/ellpack_page.cu
index 0ccd7a08138b..7097df405f54 100644
--- a/src/data/ellpack_page.cu
+++ b/src/data/ellpack_page.cu
@@ -131,7 +131,7 @@ EllpackPageImpl::EllpackPageImpl(Context const* ctx, DMatrix* dmat, const BatchP
   monitor_.Start("Quantiles");
   // Create the quantile sketches for the dmatrix and initialize HistogramCuts.
   row_stride = GetRowStride(dmat);
-  cuts_ = common::DeviceSketch(ctx->gpu_id, dmat, param.max_bin);
+  cuts_ = common::DeviceSketch(ctx, dmat, param.max_bin);
   monitor_.Stop("Quantiles");
 
   monitor_.Start("InitCompressedData");
diff --git a/src/data/gradient_index.cc b/src/data/gradient_index.cc
index 1d47ae9e6c63..1ee1bd60ba09 100644
--- a/src/data/gradient_index.cc
+++ b/src/data/gradient_index.cc
@@ -21,7 +21,7 @@ GHistIndexMatrix::GHistIndexMatrix() : columns_{std::make_unique<common::ColumnM
 
 GHistIndexMatrix::GHistIndexMatrix(Context const *ctx, DMatrix *p_fmat, bst_bin_t max_bins_per_feat,
                                    double sparse_thresh, bool sorted_sketch,
-                                   common::Span<float> hess)
+                                   common::Span<float const> hess)
     : max_numeric_bins_per_feat{max_bins_per_feat} {
   CHECK(p_fmat->SingleColBlock());
   // We use sorted sketching for approx tree method since it's more efficient in
diff --git a/src/data/gradient_index.h b/src/data/gradient_index.h
index 901451ad908e..0bb93fc20900 100644
--- a/src/data/gradient_index.h
+++ b/src/data/gradient_index.h
@@ -160,7 +160,7 @@ class GHistIndexMatrix {
    * \brief Constrcutor for SimpleDMatrix.
    */
   GHistIndexMatrix(Context const* ctx, DMatrix* x, bst_bin_t max_bins_per_feat,
-                   double sparse_thresh, bool sorted_sketch, common::Span<float> hess = {});
+                   double sparse_thresh, bool sorted_sketch, common::Span<float const> hess = {});
   /**
    * \brief Constructor for Iterative DMatrix. Initialize basic information and prepare
    *        for push batch.
diff --git a/src/data/sparse_page_dmatrix.cu b/src/data/sparse_page_dmatrix.cu
index 38304f72509e..1d9af9f06d25 100644
--- a/src/data/sparse_page_dmatrix.cu
+++ b/src/data/sparse_page_dmatrix.cu
@@ -25,8 +25,8 @@ BatchSet<EllpackPage> SparsePageDMatrix::GetEllpackBatches(Context const* ctx,
     cache_info_.erase(id);
     MakeCache(this, ".ellpack.page", cache_prefix_, &cache_info_);
     std::unique_ptr<common::HistogramCuts> cuts;
-    cuts = std::make_unique<common::HistogramCuts>(
-        common::DeviceSketch(ctx->gpu_id, this, param.max_bin, 0));
+    cuts =
+        std::make_unique<common::HistogramCuts>(common::DeviceSketch(ctx, this, param.max_bin, 0));
     this->InitializeSparsePage(ctx);  // reset after use.
 
     row_stride = GetRowStride(this);
diff --git a/tests/cpp/common/test_hist_util.cu b/tests/cpp/common/test_hist_util.cu
index 2d5735925565..91baad981f64 100644
--- a/tests/cpp/common/test_hist_util.cu
+++ b/tests/cpp/common/test_hist_util.cu
@@ -3,17 +3,22 @@
  */
 #include <gtest/gtest.h>
 #include <thrust/device_vector.h>
+#include <xgboost/base.h>  // for bst_bin_t
 #include <xgboost/c_api.h>
 #include <xgboost/data.h>
 
-#include <algorithm>
-#include <cmath>
+#include <algorithm>  // for transform
+#include <cmath>      // for floor
+#include <cstddef>    // for size_t
+#include <limits>     // for numeric_limits
+#include <string>     // for string, to_string
+#include <tuple>      // for tuple, make_tuple
+#include <vector>     // for vector
 
 #include "../../../include/xgboost/logging.h"
 #include "../../../src/common/device_helpers.cuh"
 #include "../../../src/common/hist_util.cuh"
 #include "../../../src/common/hist_util.h"
-#include "../../../src/common/math.h"
 #include "../../../src/data/device_adapter.cuh"
 #include "../../../src/data/simple_dmatrix.h"
 #include "../data/test_array_interface.h"
@@ -21,8 +26,7 @@
 #include "../helpers.h"
 #include "test_hist_util.h"
 
-namespace xgboost {
-namespace common {
+namespace xgboost::common {
 
 template <typename AdapterT>
 HistogramCuts GetHostCuts(Context const* ctx, AdapterT* adapter, int num_bins, float missing) {
@@ -32,16 +36,17 @@ HistogramCuts GetHostCuts(Context const* ctx, AdapterT* adapter, int num_bins, f
 }
 
 TEST(HistUtil, DeviceSketch) {
+  auto ctx = MakeCUDACtx(0);
   int num_columns = 1;
   int num_bins = 4;
   std::vector<float> x = {1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 7.0f, -1.0f};
   int num_rows = x.size();
   auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
 
-  auto device_cuts = DeviceSketch(0, dmat.get(), num_bins);
+  auto device_cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
 
-  Context ctx;
-  HistogramCuts host_cuts = SketchOnDMatrix(&ctx, dmat.get(), num_bins);
+  Context cpu_ctx;
+  HistogramCuts host_cuts = SketchOnDMatrix(&cpu_ctx, dmat.get(), num_bins);
 
   EXPECT_EQ(device_cuts.Values(), host_cuts.Values());
   EXPECT_EQ(device_cuts.Ptrs(), host_cuts.Ptrs());
@@ -65,6 +70,7 @@ TEST(HistUtil, SketchBatchNumElements) {
 }
 
 TEST(HistUtil, DeviceSketchMemory) {
+  auto ctx = MakeCUDACtx(0);
   int num_columns = 100;
   int num_rows = 1000;
   int num_bins = 256;
@@ -73,7 +79,7 @@ TEST(HistUtil, DeviceSketchMemory) {
 
   dh::GlobalMemoryLogger().Clear();
   ConsoleLogger::Configure({{"verbosity", "3"}});
-  auto device_cuts = DeviceSketch(0, dmat.get(), num_bins);
+  auto device_cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
 
   size_t bytes_required = detail::RequiredMemory(
       num_rows, num_columns, num_rows * num_columns, num_bins, false);
@@ -83,6 +89,7 @@ TEST(HistUtil, DeviceSketchMemory) {
 }
 
 TEST(HistUtil, DeviceSketchWeightsMemory) {
+  auto ctx = MakeCUDACtx(0);
   int num_columns = 100;
   int num_rows = 1000;
   int num_bins = 256;
@@ -92,7 +99,7 @@ TEST(HistUtil, DeviceSketchWeightsMemory) {
 
   dh::GlobalMemoryLogger().Clear();
   ConsoleLogger::Configure({{"verbosity", "3"}});
-  auto device_cuts = DeviceSketch(0, dmat.get(), num_bins);
+  auto device_cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
   ConsoleLogger::Configure({{"verbosity", "0"}});
 
   size_t bytes_required = detail::RequiredMemory(
@@ -102,43 +109,44 @@ TEST(HistUtil, DeviceSketchWeightsMemory) {
 }
 
 TEST(HistUtil, DeviceSketchDeterminism) {
+  auto ctx = MakeCUDACtx(0);
   int num_rows = 500;
   int num_columns = 5;
   int num_bins = 256;
   auto x = GenerateRandom(num_rows, num_columns);
   auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
-  auto reference_sketch = DeviceSketch(0, dmat.get(), num_bins);
+  auto reference_sketch = DeviceSketch(&ctx, dmat.get(), num_bins);
   size_t constexpr kRounds{ 100 };
   for (size_t r = 0; r < kRounds; ++r) {
-    auto new_sketch = DeviceSketch(0, dmat.get(), num_bins);
+    auto new_sketch = DeviceSketch(&ctx, dmat.get(), num_bins);
     ASSERT_EQ(reference_sketch.Values(), new_sketch.Values());
     ASSERT_EQ(reference_sketch.MinValues(), new_sketch.MinValues());
   }
 }
 
 TEST(HistUtil, DeviceSketchCategoricalAsNumeric) {
-  int categorical_sizes[] = {2, 6, 8, 12};
+  auto ctx = MakeCUDACtx(0);
+  auto categorical_sizes = {2, 6, 8, 12};
   int num_bins = 256;
-  int sizes[] = {25, 100, 1000};
+  auto sizes = {25, 100, 1000};
   for (auto n : sizes) {
     for (auto num_categories : categorical_sizes) {
       auto x = GenerateRandomCategoricalSingleColumn(n, num_categories);
       auto dmat = GetDMatrixFromData(x, n, 1);
-      auto cuts = DeviceSketch(0, dmat.get(), num_bins);
+      auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
 }
 
 TEST(HistUtil, DeviceSketchCategoricalFeatures) {
-  TestCategoricalSketch(1000, 256, 32, false,
-                        [](DMatrix *p_fmat, int32_t num_bins) {
-                          return DeviceSketch(0, p_fmat, num_bins);
-                        });
-  TestCategoricalSketch(1000, 256, 32, true,
-                        [](DMatrix *p_fmat, int32_t num_bins) {
-                          return DeviceSketch(0, p_fmat, num_bins);
-                        });
+  auto ctx = MakeCUDACtx(0);
+  TestCategoricalSketch(1000, 256, 32, false, [ctx](DMatrix* p_fmat, int32_t num_bins) {
+    return DeviceSketch(&ctx, p_fmat, num_bins);
+  });
+  TestCategoricalSketch(1000, 256, 32, true, [ctx](DMatrix* p_fmat, int32_t num_bins) {
+    return DeviceSketch(&ctx, p_fmat, num_bins);
+  });
 }
 
 void TestMixedSketch() {
@@ -162,7 +170,8 @@ void TestMixedSketch() {
   m->Info().feature_types.HostVector().push_back(FeatureType::kCategorical);
   m->Info().feature_types.HostVector().push_back(FeatureType::kNumerical);
 
-  auto cuts = DeviceSketch(0, m.get(), n_bins);
+  auto ctx = MakeCUDACtx(0);
+  auto cuts = DeviceSketch(&ctx, m.get(), n_bins);
   ASSERT_EQ(cuts.Values().size(), n_bins + n_categories);
 }
 
@@ -234,37 +243,40 @@ TEST(HistUtil, RemoveDuplicatedCategories) {
 }
 
 TEST(HistUtil, DeviceSketchMultipleColumns) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto ctx = MakeCUDACtx(0);
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns = 5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
     auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
     for (auto num_bins : bin_sizes) {
-      auto cuts = DeviceSketch(0, dmat.get(), num_bins);
+      auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
 }
 
 TEST(HistUtil, DeviceSketchMultipleColumnsWeights) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto ctx = MakeCUDACtx(0);
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns = 5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
     auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
     dmat->Info().weights_.HostVector() = GenerateRandomWeights(num_rows);
     for (auto num_bins : bin_sizes) {
-      auto cuts = DeviceSketch(0, dmat.get(), num_bins);
+      auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
 }
 
 TEST(HistUitl, DeviceSketchWeights) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto ctx = MakeCUDACtx(0);
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns = 5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
@@ -274,8 +286,8 @@ TEST(HistUitl, DeviceSketchWeights) {
     h_weights.resize(num_rows);
     std::fill(h_weights.begin(), h_weights.end(), 1.0f);
     for (auto num_bins : bin_sizes) {
-      auto cuts = DeviceSketch(0, dmat.get(), num_bins);
-      auto wcuts = DeviceSketch(0, weighted_dmat.get(), num_bins);
+      auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
+      auto wcuts = DeviceSketch(&ctx, weighted_dmat.get(), num_bins);
       ASSERT_EQ(cuts.MinValues(), wcuts.MinValues());
       ASSERT_EQ(cuts.Ptrs(), wcuts.Ptrs());
       ASSERT_EQ(cuts.Values(), wcuts.Values());
@@ -286,14 +298,15 @@ TEST(HistUitl, DeviceSketchWeights) {
 }
 
 TEST(HistUtil, DeviceSketchBatches) {
+  auto ctx = MakeCUDACtx(0);
   int num_bins = 256;
   int num_rows = 5000;
-  int batch_sizes[] = {0, 100, 1500, 6000};
+  auto batch_sizes = {0, 100, 1500, 6000};
   int num_columns = 5;
   for (auto batch_size : batch_sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
     auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
-    auto cuts = DeviceSketch(0, dmat.get(), num_bins, batch_size);
+    auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins, batch_size);
     ValidateCuts(cuts, dmat.get(), num_bins);
   }
 
@@ -301,8 +314,8 @@ TEST(HistUtil, DeviceSketchBatches) {
   size_t batches = 16;
   auto x = GenerateRandom(num_rows * batches, num_columns);
   auto dmat = GetDMatrixFromData(x, num_rows * batches, num_columns);
-  auto cuts_with_batches = DeviceSketch(0, dmat.get(), num_bins, num_rows);
-  auto cuts = DeviceSketch(0, dmat.get(), num_bins, 0);
+  auto cuts_with_batches = DeviceSketch(&ctx, dmat.get(), num_bins, num_rows);
+  auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins, 0);
 
   auto const& cut_values_batched = cuts_with_batches.Values();
   auto const& cut_values = cuts.Values();
@@ -313,15 +326,16 @@ TEST(HistUtil, DeviceSketchBatches) {
 }
 
 TEST(HistUtil, DeviceSketchMultipleColumnsExternal) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto ctx = MakeCUDACtx(0);
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns =5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
     dmlc::TemporaryDirectory temp;
     auto dmat = GetExternalMemoryDMatrixFromData(x, num_rows, num_columns, temp);
     for (auto num_bins : bin_sizes) {
-      auto cuts = DeviceSketch(0, dmat.get(), num_bins);
+      auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
@@ -329,8 +343,9 @@ TEST(HistUtil, DeviceSketchMultipleColumnsExternal) {
 
 // See https://github.com/dmlc/xgboost/issues/5866.
 TEST(HistUtil, DeviceSketchExternalMemoryWithWeights) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto ctx = MakeCUDACtx(0);
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns = 5;
   dmlc::TemporaryDirectory temp;
   for (auto num_rows : sizes) {
@@ -338,7 +353,7 @@ TEST(HistUtil, DeviceSketchExternalMemoryWithWeights) {
     auto dmat = GetExternalMemoryDMatrixFromData(x, num_rows, num_columns, temp);
     dmat->Info().weights_.HostVector() = GenerateRandomWeights(num_rows);
     for (auto num_bins : bin_sizes) {
-      auto cuts = DeviceSketch(0, dmat.get(), num_bins);
+      auto cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
@@ -504,9 +519,9 @@ void TestCategoricalSketchAdapter(size_t n, size_t num_categories,
 }
 
 TEST(HistUtil, AdapterDeviceSketchCategorical) {
-  int categorical_sizes[] = {2, 6, 8, 12};
+  auto categorical_sizes = {2, 6, 8, 12};
   int num_bins = 256;
-  int sizes[] = {25, 100, 1000};
+  auto sizes = {25, 100, 1000};
   for (auto n : sizes) {
     for (auto num_categories : categorical_sizes) {
       auto x = GenerateRandomCategoricalSingleColumn(n, num_categories);
@@ -521,8 +536,8 @@ TEST(HistUtil, AdapterDeviceSketchCategorical) {
 }
 
 TEST(HistUtil, AdapterDeviceSketchMultipleColumns) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns = 5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
@@ -538,7 +553,7 @@ TEST(HistUtil, AdapterDeviceSketchMultipleColumns) {
 TEST(HistUtil, AdapterDeviceSketchBatches) {
   int num_bins = 256;
   int num_rows = 5000;
-  int batch_sizes[] = {0, 100, 1500, 6000};
+  auto batch_sizes = {0, 100, 1500, 6000};
   int num_columns = 5;
   for (auto batch_size : batch_sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
@@ -619,14 +634,15 @@ TEST(HistUtil, GetColumnSize) {
 // Check sketching from adapter or DMatrix results in the same answer
 // Consistency here is useful for testing and user experience
 TEST(HistUtil, SketchingEquivalent) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  auto ctx = MakeCUDACtx(0);
+  auto bin_sizes = {2, 16, 256, 512};
+  auto sizes = {100, 1000, 1500};
   int num_columns = 5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
     auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
     for (auto num_bins : bin_sizes) {
-      auto dmat_cuts = DeviceSketch(0, dmat.get(), num_bins);
+      auto dmat_cuts = DeviceSketch(&ctx, dmat.get(), num_bins);
       auto x_device = thrust::device_vector<float>(x);
       auto adapter = AdapterFromData(x_device, num_rows, num_columns);
       common::HistogramCuts adapter_cuts = MakeUnweightedCutsForTest(
@@ -641,21 +657,25 @@ TEST(HistUtil, SketchingEquivalent) {
 }
 
 TEST(HistUtil, DeviceSketchFromGroupWeights) {
+  auto ctx = MakeCUDACtx(0);
   size_t constexpr kRows = 3000, kCols = 200, kBins = 256;
   size_t constexpr kGroups = 10;
   auto m = RandomDataGenerator{kRows, kCols, 0}.GenerateDMatrix();
+
+  // sketch with group weight
   auto& h_weights = m->Info().weights_.HostVector();
-  h_weights.resize(kRows);
+  h_weights.resize(kGroups);
   std::fill(h_weights.begin(), h_weights.end(), 1.0f);
   std::vector<bst_group_t> groups(kGroups);
   for (size_t i = 0; i < kGroups; ++i) {
     groups[i] = kRows / kGroups;
   }
   m->SetInfo("group", groups.data(), DataType::kUInt32, kGroups);
-  HistogramCuts weighted_cuts = DeviceSketch(0, m.get(), kBins, 0);
+  HistogramCuts weighted_cuts = DeviceSketch(&ctx, m.get(), kBins, 0);
 
+  // sketch with no weight
   h_weights.clear();
-  HistogramCuts cuts = DeviceSketch(0, m.get(), kBins, 0);
+  HistogramCuts cuts = DeviceSketch(&ctx, m.get(), kBins, 0);
 
   ASSERT_EQ(cuts.Values().size(), weighted_cuts.Values().size());
   ASSERT_EQ(cuts.MinValues().size(), weighted_cuts.MinValues().size());
@@ -723,9 +743,10 @@ void TestAdapterSketchFromWeights(bool with_group) {
   ASSERT_EQ(cuts.Ptrs().size(), kCols + 1);
   ValidateCuts(cuts, dmat.get(), kBins);
 
+  auto cuda_ctx = MakeCUDACtx(0);
   if (with_group) {
     dmat->Info().weights_ = decltype(dmat->Info().weights_)();  // remove weight
-    HistogramCuts non_weighted = DeviceSketch(0, dmat.get(), kBins, 0);
+    HistogramCuts non_weighted = DeviceSketch(&cuda_ctx, dmat.get(), kBins, 0);
     for (size_t i = 0; i < cuts.Values().size(); ++i) {
       ASSERT_EQ(cuts.Values()[i], non_weighted.Values()[i]);
     }
@@ -760,5 +781,156 @@ TEST(HistUtil, AdapterSketchFromWeights) {
   TestAdapterSketchFromWeights(false);
   TestAdapterSketchFromWeights(true);
 }
-}  // namespace common
-}  // namespace xgboost
+
+namespace {
+class DeviceSketchWithHessianTest
+    : public ::testing::TestWithParam<std::tuple<bool, bst_row_t, bst_bin_t>> {
+  bst_feature_t n_features_ = 5;
+  bst_group_t n_groups_{3};
+
+  auto GenerateHessian(Context const* ctx, bst_row_t n_samples) const {
+    HostDeviceVector<float> hessian;
+    auto& h_hess = hessian.HostVector();
+    h_hess = GenerateRandomWeights(n_samples);
+    std::mt19937 rng(0);
+    std::shuffle(h_hess.begin(), h_hess.end(), rng);
+    hessian.SetDevice(ctx->Device());
+    return hessian;
+  }
+
+  void CheckReg(Context const* ctx, std::shared_ptr<DMatrix> p_fmat, bst_bin_t n_bins,
+                HostDeviceVector<float> const& hessian, std::vector<float> const& w,
+                std::size_t n_elements) const {
+    auto const& h_hess = hessian.ConstHostVector();
+    {
+      auto& h_weight = p_fmat->Info().weights_.HostVector();
+      h_weight = w;
+    }
+
+    HistogramCuts cuts_hess =
+        DeviceSketchWithHessian(ctx, p_fmat.get(), n_bins, hessian.ConstDeviceSpan(), n_elements);
+    ValidateCuts(cuts_hess, p_fmat.get(), n_bins);
+
+    // merge hessian
+    {
+      auto& h_weight = p_fmat->Info().weights_.HostVector();
+      ASSERT_EQ(h_weight.size(), h_hess.size());
+      for (std::size_t i = 0; i < h_weight.size(); ++i) {
+        h_weight[i] = w[i] * h_hess[i];
+      }
+    }
+
+    HistogramCuts cuts_wh = DeviceSketch(ctx, p_fmat.get(), n_bins, n_elements);
+    ValidateCuts(cuts_wh, p_fmat.get(), n_bins);
+    ASSERT_EQ(cuts_hess.Values().size(), cuts_wh.Values().size());
+    for (std::size_t i = 0; i < cuts_hess.Values().size(); ++i) {
+      ASSERT_NEAR(cuts_wh.Values()[i], cuts_hess.Values()[i], kRtEps);
+    }
+
+    p_fmat->Info().weights_.HostVector() = w;
+  }
+
+ protected:
+  Context ctx_ = MakeCUDACtx(0);
+
+  void TestLTR(Context const* ctx, bst_row_t n_samples, bst_bin_t n_bins,
+               std::size_t n_elements) const {
+    auto x = GenerateRandom(n_samples, n_features_);
+
+    std::vector<bst_group_t> gptr;
+    gptr.resize(n_groups_ + 1, 0);
+    gptr[1] = n_samples / n_groups_;
+    gptr[2] = n_samples / n_groups_ + gptr[1];
+    gptr.back() = n_samples;
+
+    auto hessian = this->GenerateHessian(ctx, n_samples);
+    auto const& h_hess = hessian.ConstHostVector();
+    auto p_fmat = GetDMatrixFromData(x, n_samples, n_features_);
+    p_fmat->Info().group_ptr_ = gptr;
+
+    // test with constant group weight
+    std::vector<float> w(n_groups_, 1.0f);
+    p_fmat->Info().weights_.HostVector() = w;
+    HistogramCuts cuts_hess =
+        DeviceSketchWithHessian(ctx, p_fmat.get(), n_bins, hessian.ConstDeviceSpan(), n_elements);
+    // make validation easier by converting it into sample weight.
+    p_fmat->Info().weights_.HostVector() = h_hess;
+    p_fmat->Info().group_ptr_.clear();
+    ValidateCuts(cuts_hess, p_fmat.get(), n_bins);
+    // restore ltr properties
+    p_fmat->Info().weights_.HostVector() = w;
+    p_fmat->Info().group_ptr_ = gptr;
+
+    // test with random group weight
+    w = GenerateRandomWeights(n_groups_);
+    p_fmat->Info().weights_.HostVector() = w;
+    cuts_hess =
+        DeviceSketchWithHessian(ctx, p_fmat.get(), n_bins, hessian.ConstDeviceSpan(), n_elements);
+    // make validation easier by converting it into sample weight.
+    p_fmat->Info().weights_.HostVector() = h_hess;
+    p_fmat->Info().group_ptr_.clear();
+    ValidateCuts(cuts_hess, p_fmat.get(), n_bins);
+
+    // merge hessian with sample weight
+    p_fmat->Info().weights_.Resize(n_samples);
+    p_fmat->Info().group_ptr_.clear();
+    for (std::size_t i = 0; i < h_hess.size(); ++i) {
+      auto gidx = dh::SegmentId(Span{gptr.data(), gptr.size()}, i);
+      p_fmat->Info().weights_.HostVector()[i] = w[gidx] * h_hess[i];
+    }
+    auto cuts = DeviceSketch(ctx, p_fmat.get(), n_bins, n_elements);
+    ValidateCuts(cuts, p_fmat.get(), n_bins);
+    ASSERT_EQ(cuts.Values().size(), cuts_hess.Values().size());
+    for (std::size_t i = 0; i < cuts.Values().size(); ++i) {
+      EXPECT_NEAR(cuts.Values()[i], cuts_hess.Values()[i], 1e-4f);
+    }
+  }
+
+  void TestRegression(Context const* ctx, bst_row_t n_samples, bst_bin_t n_bins,
+                      std::size_t n_elements) const {
+    auto x = GenerateRandom(n_samples, n_features_);
+    auto p_fmat = GetDMatrixFromData(x, n_samples, n_features_);
+    std::vector<float> w = GenerateRandomWeights(n_samples);
+
+    auto hessian = this->GenerateHessian(ctx, n_samples);
+
+    this->CheckReg(ctx, p_fmat, n_bins, hessian, w, n_elements);
+  }
+};
+
+auto MakeParamsForTest() {
+  std::vector<bst_row_t> sizes = {1, 2, 256, 512, 1000, 1500};
+  std::vector<bst_bin_t> bin_sizes = {2, 16, 256, 512};
+  std::vector<std::tuple<bool, bst_row_t, bst_bin_t>> configs;
+  for (auto n_samples : sizes) {
+    for (auto n_bins : bin_sizes) {
+      configs.emplace_back(true, n_samples, n_bins);
+      configs.emplace_back(false, n_samples, n_bins);
+    }
+  }
+  return configs;
+}
+}  // namespace
+
+TEST_P(DeviceSketchWithHessianTest, DeviceSketchWithHessian) {
+  auto param = GetParam();
+  auto n_samples = std::get<1>(param);
+  auto n_bins = std::get<2>(param);
+  if (std::get<0>(param)) {
+    this->TestLTR(&ctx_, n_samples, n_bins, 0);
+    this->TestLTR(&ctx_, n_samples, n_bins, 512);
+  } else {
+    this->TestRegression(&ctx_, n_samples, n_bins, 0);
+    this->TestRegression(&ctx_, n_samples, n_bins, 512);
+  }
+}
+
+INSTANTIATE_TEST_SUITE_P(
+    HistUtil, DeviceSketchWithHessianTest, ::testing::ValuesIn(MakeParamsForTest()),
+    [](::testing::TestParamInfo<DeviceSketchWithHessianTest::ParamType> const& info) {
+      auto task = std::get<0>(info.param) ? "ltr" : "reg";
+      auto n_samples = std::to_string(std::get<1>(info.param));
+      auto n_bins = std::to_string(std::get<2>(info.param));
+      return std::string{task} + "_" + n_samples + "_" + n_bins;
+    });
+}  // namespace xgboost::common
diff --git a/tests/cpp/common/test_quantile.cu b/tests/cpp/common/test_quantile.cu
index d2dc802a93e4..eda55ee479da 100644
--- a/tests/cpp/common/test_quantile.cu
+++ b/tests/cpp/common/test_quantile.cu
@@ -1,9 +1,14 @@
+/**
+ * Copyright 2020-2023, XGBoost contributors
+ */
 #include <gtest/gtest.h>
-#include "test_quantile.h"
-#include "../helpers.h"
+
 #include "../../../src/collective/communicator-inl.cuh"
 #include "../../../src/common/hist_util.cuh"
 #include "../../../src/common/quantile.cuh"
+#include "../../../src/data/device_adapter.cuh"  // CupyAdapter
+#include "../helpers.h"
+#include "test_quantile.h"
 
 namespace xgboost {
 namespace {
@@ -437,13 +442,13 @@ void TestColumnSplitBasic() {
   }()};
 
   // Generate cuts for distributed environment.
-  auto const device = rank;
-  HistogramCuts distributed_cuts = common::DeviceSketch(device, m.get(), kBins);
+  auto ctx = MakeCUDACtx(rank);
+  HistogramCuts distributed_cuts = common::DeviceSketch(&ctx, m.get(), kBins);
 
   // Generate cuts for single node environment
   collective::Finalize();
   CHECK_EQ(collective::GetWorldSize(), 1);
-  HistogramCuts single_node_cuts = common::DeviceSketch(device, m.get(), kBins);
+  HistogramCuts single_node_cuts = common::DeviceSketch(&ctx, m.get(), kBins);
 
   auto const& sptrs = single_node_cuts.Ptrs();
   auto const& dptrs = distributed_cuts.Ptrs();