diff --git a/egs/librispeech/asr/simple_v1/mmi_att_transformer_decode.py b/egs/librispeech/asr/simple_v1/mmi_att_transformer_decode.py
index 76c7cc08..86b05c74 100755
--- a/egs/librispeech/asr/simple_v1/mmi_att_transformer_decode.py
+++ b/egs/librispeech/asr/simple_v1/mmi_att_transformer_decode.py
@@ -71,6 +71,7 @@
 from snowfall.models.contextnet import ContextNet
 from snowfall.training.ctc_graph import build_ctc_topo
 from snowfall.training.mmi_graph import create_bigram_phone_lm
+from snowfall.training.mmi_graph import create_unigram_phone_lm
 from snowfall.training.mmi_graph import get_phone_symbols
 
 def nbest_decoding(lats: k2.Fsa, num_paths: int):
@@ -401,6 +402,15 @@ def get_parser():
         type=str2bool,
         default=True,
         help='When enabled, it uses vgg style network for subsampling')
+
+    parser.add_argument(
+        '--use-unigram-lm',
+        type=str2bool,
+        default=False,
+        help='True to use unigram LM for P. False to use bigram LM for P. '
+             'This is used only for checkpoint-loading.'
+    )
+
     return parser
 
 
@@ -423,7 +433,10 @@ def main():
 
     output_beam_size = args.output_beam_size
 
-    exp_dir = Path('exp-' + model_type + '-mmi-att-sa-vgg-normlayer')
+    if args.use_unigram_lm:
+        exp_dir = Path('exp-' + model_type + '-mmi-att-sa-vgg-normlayer-unigram')
+    else:
+        exp_dir = Path('exp-' + model_type + '-mmi-att-sa-vgg-normlayer')
     setup_logger('{}/log/log-decode'.format(exp_dir), log_level='debug')
 
     logging.info(f'output_beam_size: {output_beam_size}')
@@ -434,7 +447,12 @@ def main():
     phone_symbol_table = k2.SymbolTable.from_file(lang_dir / 'phones.txt')
 
     phone_ids = get_phone_symbols(phone_symbol_table)
-    P = create_bigram_phone_lm(phone_ids)
+    if args.use_unigram_lm:
+        logging.info('Use unigram LM for P')
+        P = create_unigram_phone_lm(phone_ids)
+    else:
+        logging.info('Use bigram LM for P')
+        P = create_bigram_phone_lm(phone_ids)
 
     phone_ids_with_blank = [0] + phone_ids
     ctc_topo = k2.arc_sort(build_ctc_topo(phone_ids_with_blank))
diff --git a/egs/librispeech/asr/simple_v1/mmi_att_transformer_train.py b/egs/librispeech/asr/simple_v1/mmi_att_transformer_train.py
index f9526481..3601843d 100755
--- a/egs/librispeech/asr/simple_v1/mmi_att_transformer_train.py
+++ b/egs/librispeech/asr/simple_v1/mmi_att_transformer_train.py
@@ -44,6 +44,7 @@
 from snowfall.training.diagnostics import measure_gradient_norms, optim_step_and_measure_param_change
 from snowfall.training.mmi_graph import MmiTrainingGraphCompiler
 from snowfall.training.mmi_graph import create_bigram_phone_lm
+from snowfall.training.mmi_graph import create_unigram_phone_lm
 
 
 def get_objf(batch: Dict,
@@ -461,6 +462,14 @@ def get_parser():
              'so that they can be simply loaded with torch.jit.load(). '
              '-1 disables this option.'
     )
+
+    parser.add_argument(
+        '--use-unigram-lm',
+        type=str2bool,
+        default=False,
+        help='True to use unigram LM for P. False to use bigram LM for P.'
+    )
+
     return parser
 
 
@@ -487,7 +496,10 @@ def run(rank, world_size, args):
     fix_random_seed(42)
     setup_dist(rank, world_size, args.master_port)
 
-    exp_dir = Path('exp-' + model_type + '-mmi-att-sa-vgg-normlayer')
+    if args.use_unigram_lm:
+        exp_dir = Path('exp-' + model_type + '-mmi-att-sa-vgg-normlayer-unigram')
+    else:
+        exp_dir = Path('exp-' + model_type + '-mmi-att-sa-vgg-normlayer')
     setup_logger(f'{exp_dir}/log/log-train-{rank}')
     if args.tensorboard and rank == 0:
         tb_writer = SummaryWriter(log_dir=f'{exp_dir}/tensorboard')
@@ -507,7 +519,14 @@ def run(rank, world_size, args):
         device=device,
     )
     phone_ids = lexicon.phone_symbols()
-    P = create_bigram_phone_lm(phone_ids)
+
+    if args.use_unigram_lm:
+        logging.info('Use unigram LM for P')
+        P = create_unigram_phone_lm(phone_ids)
+    else:
+        logging.info('Use bigram LM for P')
+        P = create_bigram_phone_lm(phone_ids)
+
     P.scores = torch.zeros_like(P.scores)
     P = P.to(device)
 
diff --git a/snowfall/training/mmi_graph.py b/snowfall/training/mmi_graph.py
index 758830f7..c970bbb3 100644
--- a/snowfall/training/mmi_graph.py
+++ b/snowfall/training/mmi_graph.py
@@ -38,7 +38,33 @@ def create_bigram_phone_lm(phones: List[int]) -> k2.Fsa:
             rules += f'{i} {j} {phones[j-1]} 0.0\n'
         rules += f'{i} {final_state} -1 0.0\n'
     rules += f'{final_state}'
-    return k2.Fsa.from_str(rules)
+    ans = k2.Fsa.from_str(rules)
+    return k2.arc_sort(ans)
+
+def create_unigram_phone_lm(phones: List[int]) -> k2.Fsa:
+    '''Create a unigram phone LM.
+    The resulting FSA (P) has two states: a start state and a
+    final state. For each phone, there is a corresponding self-loop
+    at the start state.
+
+    Caution:
+      blank is not a phone.
+
+    Args:
+      A list of phone IDs.
+
+    Returns:
+      An FSA representing the unigram phone LM.
+    '''
+    assert 0 not in phones
+
+    rules = '0 1 -1 0.0\n'
+    for i in phones:
+        rules += f'0 0 {i} 0.0\n'
+    rules += '1\n'
+
+    ans = k2.Fsa.from_str(rules)
+    return k2.arc_sort(ans)
 
 
 class MmiTrainingGraphCompiler(object):