diff --git a/sdm/models/kumo/tabular/icl.py b/sdm/models/kumo/tabular/icl.py
index be431353d..067d5f619 100644
--- a/sdm/models/kumo/tabular/icl.py
+++ b/sdm/models/kumo/tabular/icl.py
@@ -74,6 +74,7 @@ def forward(
                 y_emb = self.y_lin(y.unsqueeze(-1))  # [..., R_train, D]
 
             x[..., :R_train, :] += y_emb.to(x.dtype)
+            del y_emb
 
         for i, layer in enumerate(self.layers):
             cache_key = f"icl_block.layer{i}"
@@ -117,12 +118,14 @@ def forward(
                 if last_layer
                 else x[..., :R_train, :],
             )
+            key_value = KVCacheEntry(
+                key=key[..., : self.kv_heads, :].contiguous(),
+                value=value[..., : self.kv_heads, :].contiguous(),
+            )
+            del key, value
             x_query = layer(
                 query=x[..., R_train:, :],
-                key_value=KVCacheEntry(
-                    key=key[..., : self.kv_heads, :].contiguous(),
-                    value=value[..., : self.kv_heads, :].contiguous(),
-                ),
+                key_value=key_value,
                 out=None if torch.is_grad_enabled() else x[..., R_train:, :],
             )
             if last_layer:
diff --git a/sdm/models/kumo/tabular/row_embedding.py b/sdm/models/kumo/tabular/row_embedding.py
index f69ff3e0e..ccbb0afff 100644
--- a/sdm/models/kumo/tabular/row_embedding.py
+++ b/sdm/models/kumo/tabular/row_embedding.py
@@ -3,12 +3,14 @@
 
 # ruff: noqa: D101, D102
 
+import math
 from typing import Any, cast
 
 import torch
 from torch import Tensor
 from torch.nn import Embedding, Linear, ModuleList, Parameter
 
+from sdm._memory import chunk_memory_limit
 from sdm.cache import Cache, KVCacheEntry
 from sdm.models.kumo.tabular.block import KumoTabularTransformerBlock
 from sdm.models.kumo.tabular.cell_embedding import CellEmbedding
@@ -66,7 +68,7 @@ def __init__(
             **factory_kwargs,
         )
 
-        self.col_blocks = ModuleList(
+        self.col_blocks: ModuleList[InducedTransformerBlock] = ModuleList(
             InducedTransformerBlock(
                 channels=channels,
                 num_inducing_points=num_inducing_points,
@@ -89,7 +91,7 @@ def __init__(
             )
             for _ in range(num_layers)
         )
-        self.row_blocks = ModuleList(
+        self.row_blocks: ModuleList[KumoTabularTransformerBlock] = ModuleList(
             KumoTabularTransformerBlock(
                 channels=channels,
                 num_heads=num_heads,
@@ -114,6 +116,105 @@ def forward(
         *,
         cache: Cache | None = None,
     ) -> Tensor:  # [..., R, K * D]
+        starts = self._pass_starts(x, train_size=y.size(-1), cache=cache)
+        if len(starts) == 1:
+            return self._forward(x, y, categorical_mask, cache=cache)
+
+        # Query rows only read context state, which the first pass records
+        # for replay in later passes.
+        cache = Cache() if cache is None else cache
+        first = self._forward(
+            x=x[..., : starts[1], :],
+            y=y,
+            categorical_mask=categorical_mask,
+            cache=cache,
+        )  # [..., starts[1], K * D]
+        cache.freeze()
+        out = first.new_empty((*first.shape[:-2], x.size(-2), first.size(-1)))
+        out[..., : starts[1], :] = first
+        del first
+        ends = [*starts[2:], x.size(-2)]
+        for start, end in zip(starts[1:], ends, strict=True):
+            out[..., start:end, :] = self._forward(
+                x=x[..., start:end, :],
+                y=y[..., :0],
+                categorical_mask=categorical_mask,
+                cache=cache,
+            )
+        return out
+
+    def _pass_starts(
+        self,
+        x: Tensor,  # [..., R, C]
+        train_size: int,
+        cache: Cache | None,
+    ) -> list[int]:
+        # First rows of the passes that embed the rows of `x`. Passes run
+        # without gradients on CUDA and replay context state from a cache.
+        if (
+            torch.is_grad_enabled()
+            or not x.is_cuda
+            or (cache is not None and cache.is_recording)
+        ):
+            return [0]
+        *B, R, C = x.size()
+        N = math.prod(B)
+        K, D = self.readout_token.size(-2), self.channels
+        G = self.cell_embedding.group_size
+        M = self.col_blocks[0].inducing_points.size(-2)
+        s = (
+            torch.get_autocast_dtype(x.device.type).itemsize
+            if torch.is_autocast_enabled(x.device.type)
+            else x.element_size()
+        )
+        budget = chunk_memory_limit(x.device)
+        # Bytes per row: the cell buffer, plus the missingness mask, imputed
+        # values and their feature groups while embedding cells.
+        row_bytes = N * (
+            (K + C) * D * s + (G + 1) * (x.element_size() + 1) * C
+        )
+        # Without a cache, the context pass records the key/value projections
+        # of all column blocks for the query passes. Query rows that fit the
+        # chunk memory budget plus these projections run with the context.
+        state_bytes = 0
+        if cache is None:
+            state_bytes = 2 * N * C * M * D * s * len(self.col_blocks)
+        if (R - train_size) * row_bytes <= budget + state_bytes:
+            return [0]
+
+        # Row blocks run the rows of all batch entries in chunks of `chunk`
+        # rows. In passes starting on multiples of `grid` rows, every row runs
+        # in a chunk of the same size as in a single pass, since the last pass
+        # holds the partial last chunk of a single pass, the last
+        # `N * R % chunk` rows of the last batch entry. Attention over long
+        # rows rounds differently in small chunks, so this keeps passes equal
+        # to a single pass up to rare rounding differences in small passes.
+        chunk = self.row_blocks[0].auto_batch_size_limit(
+            device=x.device,
+            element_size=s,
+            query_length=K + C,
+            key_value_length=K + C,
+        )
+        grid = chunk // math.gcd(N, chunk)
+        context = -(-train_size // grid) * grid
+        last = R - max(N * R % chunk, 1)
+        if context > last:
+            return [0]
+        # Balanced query passes need no more memory than the context pass,
+        # the budget or one grid of rows, whichever is more.
+        grids = max(max(train_size, budget // row_bytes) // grid, 1)
+        num_passes = -(-(R - context) // (grids * grid))
+        step = -(-(R - context) // (num_passes * grid)) * grid
+        return [0, *range(context or step, last + 1, step)]
+
+    def _forward(
+        self,
+        x: Tensor,  # [..., R, C]
+        y: Tensor,  # [..., R_train]
+        categorical_mask: Tensor,  # [..., C]
+        *,
+        cache: Cache | None = None,
+    ) -> Tensor:  # [..., R, K * D]
 
         *B, R, C = x.size()
         R_train = y.size(-1)
diff --git a/test/models/kumo/tabular/test_model.py b/test/models/kumo/tabular/test_model.py
index 0f153a8a8..c7840478d 100644
--- a/test/models/kumo/tabular/test_model.py
+++ b/test/models/kumo/tabular/test_model.py
@@ -9,6 +9,8 @@
 import sdm.processing as sp
 from sdm import CategoricalTensor, Stype, TableTensor
 from sdm.models import KumoTabular
+from sdm.models.kumo.tabular.row_embedding import RowEmbedding
+from sdm.testing import onlyCUDA
 
 
 def _build(
@@ -90,6 +92,52 @@ def _recipe() -> sp.Recipe:
     )
 
 
+@onlyCUDA
+@pytest.mark.parametrize("task", ["classification", "regression"])
+def test_query_passes_match_single_pass(
+    task: Literal["classification", "regression"],
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    model = _build(task, "small").cuda().eval()
+    x = torch.randn(1008, 4, device="cuda")
+    x[::3, 0] = float("nan")
+    x_context, x_query = TableTensor.from_tensor(x).split([8, 1000], dim=0)
+    # 12 classes run through ECOC.
+    target = (
+        TableTensor(
+            columns={Stype.categorical: ("target",)},
+            categorical=CategoricalTensor(
+                code=torch.arange(8, device="cuda").unsqueeze(-1),
+                categories=(torch.arange(12, device="cuda"),),
+            ),
+        )
+        if task == "classification"
+        else TableTensor.from_tensor(torch.randn(8, 1, device="cuda"))
+    )
+
+    def forward() -> TableTensor:
+        return model(
+            x_context=x_context,
+            y_context=target,
+            x_query=x_query,
+            num_estimators=2,
+            generator=torch.Generator("cuda").manual_seed(0),
+        )
+
+    # A chunk memory limit of 1 MiB embeds the query rows in passes.
+    total_memory = torch.cuda.get_device_properties("cuda").total_memory
+    monkeypatch.setenv("SDM_CHUNK_MEMORY_FRACTION", str(2**20 / total_memory))
+    actual = forward()
+    monkeypatch.setattr(
+        RowEmbedding,
+        "_pass_starts",
+        lambda self, x, train_size, cache: [0],
+    )
+    expected = forward()
+
+    torch.testing.assert_close(actual.numerical, expected.numerical)
+
+
 def test_forward(
     cls_model: KumoTabular,
     reg_model: KumoTabular,
diff --git a/test/models/kumo/tabular/test_row_embedding.py b/test/models/kumo/tabular/test_row_embedding.py
index 29fa0380e..31c514271 100644
--- a/test/models/kumo/tabular/test_row_embedding.py
+++ b/test/models/kumo/tabular/test_row_embedding.py
@@ -1,11 +1,12 @@
 # SPDX-FileCopyrightText: Copyright (c) 2026, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
 # SPDX-License-Identifier: Apache-2.0
 
+import pytest
 import torch
 
 from sdm.cache import Cache
 from sdm.models.kumo.tabular.row_embedding import RowEmbedding
-from sdm.testing import withCUDA
+from sdm.testing import onlyCUDA, withCUDA
 
 
 @withCUDA
@@ -46,3 +47,103 @@ def test_row_embedding(device: torch.device) -> None:
     assert out.size() == (2, 2, 32)
     assert out.device == device
     torch.testing.assert_close(out, expected[:, 3:], atol=1e-5, rtol=1e-5)
+
+
+@onlyCUDA
+@pytest.mark.parametrize("cached", [False, True])
+def test_row_embedding_passes(
+    cached: bool,
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    encoder = RowEmbedding(
+        num_classes=0,
+        channels=16,
+        num_layers=2,
+        num_heads=2,
+        group_size=3,
+        num_frequencies=8,
+        num_inducing_points=4,
+        num_readout_tokens=2,
+        device="cuda",
+    )
+    # Randomize the zero-initialized residual branches, so that attention
+    # outputs reach the embedding.
+    for parameter in encoder.parameters():
+        if not parameter.any():
+            torch.nn.init.normal_(parameter, std=0.02)
+    # With many batch entries, e.g. estimators or ECOC tasks, a chunk of the
+    # row attention spans more rows than the chunk memory limit allows.
+    x = torch.randn(17, 64, 3, device="cuda")
+    x[x > 1.0] = torch.nan
+    y = torch.randn(17, 4, device="cuda")
+    categorical_mask = torch.tensor([True, False, False], device="cuda")
+
+    @torch.inference_mode()
+    def embed() -> torch.Tensor:
+        if not cached:
+            return encoder(x, y, categorical_mask)
+        cache = Cache()
+        encoder(x[:, :4], y, categorical_mask, cache=cache)
+        return encoder(
+            x[:, 4:],
+            y[:, :0],
+            categorical_mask,
+            cache=cache.freeze(),
+        )
+
+    expected = embed()
+    # Small, intermediate and single-pass budgets exercise pass boundaries.
+    total_memory = torch.cuda.get_device_properties("cuda").total_memory
+    for budget in (2**10, 2**14, 2**19):
+        fraction = budget / total_memory
+        monkeypatch.setenv("SDM_CHUNK_MEMORY_FRACTION", str(fraction))
+        torch.testing.assert_close(embed(), expected)
+
+
+@onlyCUDA
+def test_row_embedding_passes_on_wide_tables(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    # Attention over more than 256 row tokens splits keys and values for
+    # small batches of rows, so passes must keep the row chunks of one pass.
+    encoder = RowEmbedding(
+        num_classes=10,
+        channels=64,
+        num_layers=2,
+        num_heads=2,
+        group_size=3,
+        num_frequencies=8,
+        num_inducing_points=8,
+        num_readout_tokens=2,
+        device="cuda",
+    )
+    # Randomize the zero-initialized residual branches, so that attention
+    # outputs reach the embedding.
+    for parameter in encoder.parameters():
+        if not parameter.any():
+            torch.nn.init.normal_(parameter, std=0.02)
+    x = torch.randn(3, 1169, 300, device="cuda")
+    x[x > 2.0] = torch.nan
+    y = torch.randint(10, (3, 200), device="cuda")
+    categorical_mask = torch.arange(300, device="cuda") % 4 == 0
+
+    def embed() -> tuple[torch.Tensor, int]:
+        torch.cuda.synchronize()
+        baseline = torch.cuda.memory_allocated()
+        torch.cuda.reset_peak_memory_stats()
+        with torch.no_grad(), torch.autocast("cuda", dtype=torch.float16):
+            out = encoder(x, y, categorical_mask)
+        torch.cuda.synchronize()
+        return out, torch.cuda.max_memory_allocated() - baseline
+
+    monkeypatch.setenv("SDM_CHUNK_MEMORY_FRACTION", "0.001")
+    actual, peak = embed()
+    monkeypatch.setattr(
+        RowEmbedding,
+        "_pass_starts",
+        lambda self, x, train_size, cache: [0],
+    )
+    expected, expected_peak = embed()
+
+    assert torch.equal(actual, expected)
+    assert peak < expected_peak