diff --git a/egs/librispeech/ASR/conformer_mmi/asr_datamodule.py b/egs/librispeech/ASR/conformer_mmi/asr_datamodule.py
index 8290e71d1..d3eab87a9 100644
--- a/egs/librispeech/ASR/conformer_mmi/asr_datamodule.py
+++ b/egs/librispeech/ASR/conformer_mmi/asr_datamodule.py
@@ -162,7 +162,9 @@ class LibriSpeechAsrDataModule(DataModule):
         cuts_musan = load_manifest(self.args.feature_dir / "cuts_musan.json.gz")
 
         logging.info("About to create train dataset")
-        transforms = [CutMix(cuts=cuts_musan, prob=0.5, snr=(10, 20))]
+        transforms = [
+            CutMix(cuts=cuts_musan, prob=0.5, snr=(10, 20), preserve_id=True)
+        ]
         if self.args.concatenate_cuts:
             logging.info(
                 f"Using cut concatenation with duration factor "
diff --git a/egs/librispeech/ASR/conformer_mmi/train.py b/egs/librispeech/ASR/conformer_mmi/train.py
index 6decbc189..900d109a8 100755
--- a/egs/librispeech/ASR/conformer_mmi/train.py
+++ b/egs/librispeech/ASR/conformer_mmi/train.py
@@ -21,7 +21,7 @@ import argparse
 import logging
 from pathlib import Path
 from shutil import copyfile
-from typing import Optional
+from typing import Dict, Optional
 
 import k2
 import torch
@@ -36,6 +36,11 @@ from torch.nn.utils import clip_grad_norm_
 from torch.utils.tensorboard import SummaryWriter
 from transformer import Noam
 
+from icefall.ali import (
+    convert_alignments_to_tensor,
+    load_alignments,
+    lookup_alignments,
+)
 from icefall.checkpoint import load_checkpoint
 from icefall.checkpoint import save_checkpoint as save_checkpoint_impl
 from icefall.dist import cleanup_dist, setup_dist
@@ -93,6 +98,17 @@ def get_parser():
         """,
     )
 
+    parser.add_argument(
+        "--ali-dir",
+        type=str,
+        default="data/ali_500",
+        help="""This folder is expected to contain
+        two files, train-960.pt and valid.pt, which
+        contain framewise alignment information for
+        the training set and validation set.
+        """,
+    )
+
     return parser
 
 
@@ -284,6 +300,7 @@ def compute_loss(
     batch: dict,
     graph_compiler: MmiTrainingGraphCompiler,
     is_training: bool,
+    ali: Optional[Dict[str, torch.Tensor]],
 ):
     """
     Compute LF-MMI loss given the model and its inputs.
@@ -304,6 +321,8 @@ def compute_loss(
         True for training. False for validation. When it is True, this
         function enables autograd during computation; when it is False, it
         disables autograd.
+      ali:
+        Precomputed alignments.
     """
     device = graph_compiler.device
     feature = batch["inputs"]
@@ -323,6 +342,30 @@ def compute_loss(
             supervisions, subsampling_factor=params.subsampling_factor
         )
 
+        if ali is not None and params.batch_idx_train < 4000:
+            cut_ids = [cut.id for cut in supervisions["cut"]]
+
+            # As encode_supervisions reorders cuts, we need
+            # also to reorder cut IDs here
+            new2old = supervision_segments[:, 0].tolist()
+            cut_ids = [cut_ids[i] for i in new2old]
+
+            # Check that new2old is just a permutation,
+            # i.e., each cut contains only one utterance
+            new2old.sort()
+            assert new2old == torch.arange(len(new2old)).tolist()
+            mask = lookup_alignments(
+                cut_ids=cut_ids,
+                alignments=ali,
+                num_classes=nnet_output.shape[2],
+            ).to(nnet_output)
+
+            min_len = min(nnet_output.shape[1], mask.shape[1])
+            ali_scale = 500.0 / (params.batch_idx_train + 500)
+
+            nnet_output = nnet_output.clone()
+            nnet_output[:, :min_len, :] += ali_scale * mask[:, :min_len, :]
+
         loss_fn = LFMMILoss(
             graph_compiler=graph_compiler,
             use_pruned_intersect=params.use_pruned_intersect,
@@ -377,6 +420,7 @@ def compute_validation_loss(
     graph_compiler: MmiTrainingGraphCompiler,
     valid_dl: torch.utils.data.DataLoader,
     world_size: int = 1,
+    ali: Optional[Dict[str, torch.Tensor]] = None,
 ) -> None:
     """Run the validation process. The validation loss
     is saved in `params.valid_loss`.
@@ -394,6 +438,7 @@ def compute_validation_loss(
             batch=batch,
             graph_compiler=graph_compiler,
             is_training=False,
+            ali=ali,
         )
         assert loss.requires_grad is False
         assert mmi_loss.requires_grad is False
@@ -435,6 +480,8 @@ def train_one_epoch(
     graph_compiler: MmiTrainingGraphCompiler,
     train_dl: torch.utils.data.DataLoader,
     valid_dl: torch.utils.data.DataLoader,
+    train_ali: Optional[Dict[str, torch.Tensor]],
+    valid_ali: Optional[Dict[str, torch.Tensor]],
     tb_writer: Optional[SummaryWriter] = None,
     world_size: int = 1,
 ) -> None:
@@ -457,6 +504,10 @@ def train_one_epoch(
         Dataloader for the training dataset.
       valid_dl:
         Dataloader for the validation dataset.
+      train_ali:
+        Precomputed alignments for the training set.
+      valid_ali:
+        Precomputed alignments for the validation set.
       tb_writer:
         Writer to write log messages to tensorboard.
       world_size:
@@ -481,6 +532,7 @@ def train_one_epoch(
             batch=batch,
             graph_compiler=graph_compiler,
             is_training=True,
+            ali=train_ali,
         )
 
         # NOTE: We use reduction==sum and loss is computed over utterances
@@ -565,6 +617,7 @@ def train_one_epoch(
                 graph_compiler=graph_compiler,
                 valid_dl=valid_dl,
                 world_size=world_size,
+                ali=valid_ali,
             )
             model.train()
             logging.info(
@@ -673,12 +726,34 @@ def run(rank, world_size, args):
     if checkpoints:
         optimizer.load_state_dict(checkpoints["optimizer"])
 
+    train_960_ali_filename = Path(params.ali_dir) / "train-960.pt"
+    if params.batch_idx_train < 4000 and train_960_ali_filename.is_file():
+        logging.info("Use pre-computed alignments")
+        subsampling_factor, train_ali = load_alignments(train_960_ali_filename)
+        assert subsampling_factor == params.subsampling_factor
+        assert len(train_ali) == 843723, f"{len(train_ali)} vs 843723"
+
+        valid_ali_filename = Path(params.ali_dir) / "valid.pt"
+        subsampling_factor, valid_ali = load_alignments(valid_ali_filename)
+        assert subsampling_factor == params.subsampling_factor
+
+        train_ali = convert_alignments_to_tensor(train_ali, device=device)
+        valid_ali = convert_alignments_to_tensor(valid_ali, device=device)
+    else:
+        logging.info("Not using alignments")
+        train_ali = None
+        valid_ali = None
+
     librispeech = LibriSpeechAsrDataModule(args)
     train_dl = librispeech.train_dataloaders()
     valid_dl = librispeech.valid_dataloaders()
 
     for epoch in range(params.start_epoch, params.num_epochs):
         train_dl.sampler.set_epoch(epoch)
+        if params.batch_idx_train > 4000 and train_ali is not None:
+            # Delete the alignments to save memory
+            train_ali = None
+            valid_ali = None
 
         cur_lr = optimizer._rate
         if tb_writer is not None:
@@ -699,6 +774,8 @@ def run(rank, world_size, args):
             graph_compiler=graph_compiler,
             train_dl=train_dl,
             valid_dl=valid_dl,
+            train_ali=train_ali,
+            valid_ali=valid_ali,
             tb_writer=tb_writer,
             world_size=world_size,
         )
diff --git a/icefall/ali.py b/icefall/ali.py
new file mode 100644
index 000000000..c3e4b2662
--- /dev/null
+++ b/icefall/ali.py
@@ -0,0 +1,142 @@
+# Copyright      2021  Xiaomi Corp.        (authors: Fangjun Kuang)
+#
+# See ../../LICENSE for clarification regarding multiple authors
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from typing import Dict, List, Tuple
+
+import torch
+from torch.nn.utils.rnn import pad_sequence
+
+
+def save_alignments(
+    alignments: Dict[str, List[int]],
+    subsampling_factor: int,
+    filename: str,
+) -> None:
+    """Save alignments to a file.
+
+    Args:
+      alignments:
+        A dict containing alignments. Keys of the dict are utterances and
+        values are the corresponding framewise alignments after subsampling.
+      subsampling_factor:
+        The subsampling factor of the model.
+      filename:
+        Path to save the alignments.
+    Returns:
+      Return None.
+    """
+    ali_dict = {
+        "subsampling_factor": subsampling_factor,
+        "alignments": alignments,
+    }
+    torch.save(ali_dict, filename)
+
+
+def load_alignments(filename: str) -> Tuple[int, Dict[str, List[int]]]:
+    """Load alignments from a file.
+
+    Args:
+      filename:
+        Path to the file containing alignment information.
+        The file should be saved by :func:`save_alignments`.
+    Returns:
+      Return a tuple containing:
+        - subsampling_factor: The subsampling_factor used to compute
+          the alignments.
+        - alignments: A dict containing utterances and their corresponding
+          framewise alignment, after subsampling.
+    """
+    ali_dict = torch.load(filename)
+    subsampling_factor = ali_dict["subsampling_factor"]
+    alignments = ali_dict["alignments"]
+    return subsampling_factor, alignments
+
+
+def convert_alignments_to_tensor(
+    alignments: Dict[str, List[int]], device: torch.device
+) -> Dict[str, torch.Tensor]:
+    """Convert alignments from list of int to a 1-D torch.Tensor.
+
+    Args:
+      alignments:
+        A dict containing alignments. Keys are utterance IDs and
+        values are their corresponding frame-wise alignments.
+      device:
+        The device to move the alignments to.
+    Returns:
+      Return a dict using 1-D torch.Tensor to store the alignments.
+      The dtype of the tensor are `torch.int64`. We choose `torch.int64`
+      because `torch.nn.functional.one_hot` requires that.
+    """
+    ans = {}
+    for utt_id, ali in alignments.items():
+        ali = torch.tensor(ali, dtype=torch.int64, device=device)
+        ans[utt_id] = ali
+    return ans
+
+
+def lookup_alignments(
+    cut_ids: List[str],
+    alignments: Dict[str, torch.Tensor],
+    num_classes: int,
+    log_score: float = -10,
+) -> torch.Tensor:
+    """Return a mask constructed from alignments by a list of cut IDs.
+
+    The returned mask is a 3-D tensor of shape (N, T, C). For each frame,
+    i.e., each row, of the returned mask, positions not corresponding to
+    the alignments are filled with `log_score`, while the position
+    specified by the alignment is filled with 0. For instance, if the alignments
+    of two utterances are:
+
+        [ [1, 3, 2], [1, 0, 4, 2] ]
+    num_classes is 5 and log_score is -10,  then the returned mask is
+
+        [
+          [[-10, 0, -10, -10, -10],
+           [-10, -10, -10, 0, -10],
+           [-10, -10, 0, -10, -10],
+           [0, -10, -10, -10, -10]],
+          [[-10, 0, -10, -10, -10],
+           [0, -10, -10, -10, -10],
+           [-10, -10, -10, -10, 0],
+           [-10, -10, 0, -10, -10]]
+        ]
+    Note: We pad the alignment of the first utterance with 0.
+
+    Args:
+      cut_ids:
+        A list of utterance IDs.
+      alignments:
+        A dict containing alignments. The keys are utterance IDs and the values
+        are framewise alignments.
+      num_classes:
+        The max token ID + 1 that appears in the alignments.
+      log_score:
+        Positions in the returned tensor not corresponding to the alignments
+        are filled with this value.
+    Returns:
+      Return a 3-D torch.float32 tensor of shape (N, T, C).
+    """
+    # We assume all utterances have their alignments.
+    ali = [alignments[cut_id] for cut_id in cut_ids]
+    padded_ali = pad_sequence(ali, batch_first=True, padding_value=0)
+    padded_one_hot = torch.nn.functional.one_hot(
+        padded_ali,
+        num_classes=num_classes,
+    )
+    mask = (1 - padded_one_hot) * float(log_score)
+    return mask
diff --git a/test/test_ali.py b/test/test_ali.py
new file mode 100755
index 000000000..e8516e6dc
--- /dev/null
+++ b/test/test_ali.py
@@ -0,0 +1,223 @@
+#!/usr/bin/env python3
+# Copyright      2021  Xiaomi Corp.        (authors: Fangjun Kuang)
+#
+# See ../../LICENSE for clarification regarding multiple authors
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# Runt his file using one of the following two ways:
+#  (1) python3 ./test/test_ali.py
+#  (2) pytest ./test/test_ali.py
+
+# The purpose of this file is to show that if we build a mask
+# from alignments and add it to a randomly generated nnet_output,
+# we can decode the correct transcript.
+
+from pathlib import Path
+
+import k2
+import torch
+from lhotse import load_manifest
+from lhotse.dataset import K2SpeechRecognitionDataset, SingleCutSampler
+from torch.nn.utils.rnn import pad_sequence
+from torch.utils.data import DataLoader
+
+from icefall.ali import (
+    convert_alignments_to_tensor,
+    load_alignments,
+    lookup_alignments,
+)
+from icefall.decode import get_lattice, one_best_decoding
+from icefall.lexicon import Lexicon
+from icefall.utils import get_texts
+
+ICEFALL_DIR = Path(__file__).resolve().parent.parent
+egs_dir = ICEFALL_DIR / "egs/librispeech/ASR"
+lang_dir = egs_dir / "data/lang_bpe_500"
+#  cut_json = egs_dir / "data/fbank/cuts_train-clean-100.json.gz"
+cut_json = egs_dir / "data/fbank/cuts_train-clean-360.json.gz"
+#  cut_json = egs_dir / "data/fbank/cuts_train-other-500.json.gz"
+ali_filename = ICEFALL_DIR / "egs/librispeech/ASR/data/ali_500/train-960.pt"
+
+#  cut_json = egs_dir / "data/fbank/cuts_test-clean.json.gz"
+#  ali_filename = ICEFALL_DIR / "egs/librispeech/ASR/data/ali_500/test_clean.pt"
+
+
+def data_exists():
+    return ali_filename.exists() and cut_json.exists() and lang_dir.exists()
+
+
+def get_dataloader():
+    cuts_train = load_manifest(cut_json)
+    cuts_train = cuts_train.with_features_path_prefix(egs_dir)
+    train_sampler = SingleCutSampler(
+        cuts_train,
+        max_duration=200,
+        shuffle=False,
+    )
+
+    train = K2SpeechRecognitionDataset(return_cuts=True)
+
+    train_dl = DataLoader(
+        train,
+        sampler=train_sampler,
+        batch_size=None,
+        num_workers=1,
+        persistent_workers=False,
+    )
+    return train_dl
+
+
+def test_one_hot():
+    a = [1, 3, 2]
+    b = [1, 0, 4, 2]
+    c = [torch.tensor(a), torch.tensor(b)]
+    d = pad_sequence(c, batch_first=True, padding_value=0)
+    f = torch.nn.functional.one_hot(d, num_classes=5)
+    e = (1 - f) * -10.0
+    expected = torch.tensor(
+        [
+            [
+                [-10, 0, -10, -10, -10],
+                [-10, -10, -10, 0, -10],
+                [-10, -10, 0, -10, -10],
+                [0, -10, -10, -10, -10],
+            ],
+            [
+                [-10, 0, -10, -10, -10],
+                [0, -10, -10, -10, -10],
+                [-10, -10, -10, -10, 0],
+                [-10, -10, 0, -10, -10],
+            ],
+        ]
+    ).to(e.dtype)
+    assert torch.all(torch.eq(e, expected))
+
+
+def test():
+    """
+    The purpose of this test is to show that we can use pre-computed
+    alignments to construct a mask, adding it to a randomly generated
+    nnet_output, to decode the correct transcript from the resulting
+    nnet_output.
+    """
+    if not data_exists():
+        return
+    device = torch.device("cpu")
+    if torch.cuda.is_available():
+        device = torch.device("cuda", 0)
+    dl = get_dataloader()
+
+    subsampling_factor, ali = load_alignments(ali_filename)
+    ali = convert_alignments_to_tensor(ali, device=device)
+
+    lexicon = Lexicon(lang_dir)
+    max_token_id = max(lexicon.tokens)
+    num_classes = max_token_id + 1  # +1 for the blank
+    word_table = lexicon.word_table
+
+    HLG = k2.Fsa.from_dict(
+        torch.load(f"{lang_dir}/HLG.pt", map_location=device)
+    )
+
+    for batch in dl:
+        features = batch["inputs"]
+        supervisions = batch["supervisions"]
+        N = features.shape[0]
+        T = features.shape[1] // subsampling_factor
+        nnet_output = (
+            torch.rand(N, T, num_classes, dtype=torch.float32, device=device)
+            .softmax(dim=-1)
+            .log()
+        )
+        cut_ids = [cut.id for cut in supervisions["cut"]]
+        mask = lookup_alignments(
+            cut_ids=cut_ids, alignments=ali, num_classes=num_classes
+        )
+        min_len = min(nnet_output.shape[1], mask.shape[1])
+        ali_model_scale = 0.8
+
+        nnet_output[:, :min_len, :] += ali_model_scale * mask[:, :min_len, :]
+
+        supervisions = batch["supervisions"]
+
+        supervision_segments = torch.stack(
+            (
+                supervisions["sequence_idx"],
+                supervisions["start_frame"] // subsampling_factor,
+                supervisions["num_frames"] // subsampling_factor,
+            ),
+            1,
+        ).to(torch.int32)
+
+        lattice = get_lattice(
+            nnet_output=nnet_output,
+            HLG=HLG,
+            supervision_segments=supervision_segments,
+            search_beam=20,
+            output_beam=8,
+            min_active_states=30,
+            max_active_states=10000,
+            subsampling_factor=subsampling_factor,
+        )
+
+        best_path = one_best_decoding(lattice=lattice, use_double_scores=True)
+        hyps = get_texts(best_path)
+        hyps = [[word_table[i] for i in ids] for ids in hyps]
+        hyps = [" ".join(s) for s in hyps]
+        print(hyps)
+        print(supervisions["text"])
+        break
+
+
+def show_cut_ids():
+    # The purpose of this function is to check that
+    # for each utterance in the training set, there is
+    # a corresponding alignment.
+    #
+    # After generating a1.txt and b1.txt
+    # You can use
+    #  wc -l a1.txt b1.txt
+    # which should show the same number of lines.
+    #
+    # cat a1.txt | sort | uniq > a11.txt
+    # cat b1.txt | sort | uniq > b11.txt
+    #
+    # md5sum a11.txt b11.txt
+    #   which should show the identical hash
+    #
+    # diff a11.txt b11.txt
+    #   should print nothing
+
+    subsampling_factor, ali = load_alignments(ali_filename)
+    with open("a1.txt", "w") as f:
+        for key in ali:
+            f.write(f"{key}\n")
+
+    #  dl = get_dataloader()
+    cuts_train = (
+        load_manifest(egs_dir / "data/fbank/cuts_train-clean-100.json.gz")
+        + load_manifest(egs_dir / "data/fbank/cuts_train-clean-360.json.gz")
+        + load_manifest(egs_dir / "data/fbank/cuts_train-other-500.json.gz")
+    )
+
+    ans = []
+    for cut in cuts_train:
+        ans.append(cut.id)
+    with open("b1.txt", "w") as f:
+        for line in ans:
+            f.write(f"{line}\n")
+
+
+if __name__ == "__main__":
+    test()