diff --git a/ggml/src/ggml-cuda/convert.cu b/ggml/src/ggml-cuda/convert.cu
index 2997e2b4..2681c42e 100644
--- a/ggml/src/ggml-cuda/convert.cu
+++ b/ggml/src/ggml-cuda/convert.cu
@@ -579,7 +579,13 @@ static __global__ void convert_unary(const void * __restrict__ vx, dst_t * __res
 
     const src_t * x = (const src_t *) vx;
 
-    y[i] = x[i];
+    if constexpr (std::is_same_v<src_t, nv_bfloat16>) {
+        y[i] = __bfloat162float(x[i]);
+    } else if constexpr (std::is_same_v<dst_t, nv_bfloat16> && std::is_same_v<src_t, half>) {
+        y[i] = (float)x[i];
+    } else {
+        y[i] = x[i];
+    }
 }
 
 template <typename src_t, typename dst_t>
@@ -588,6 +594,17 @@ static void convert_unary_cuda(const void * __restrict__ vx, dst_t * __restrict_
     convert_unary<src_t><<<num_blocks, CUDA_DEQUANTIZE_BLOCK_SIZE, 0, stream>>>(vx, y, k);
 }
 
+to_bf16_cuda_t ggml_get_to_bf16_cuda(ggml_type type) {
+    switch (type) {
+        case GGML_TYPE_F32:
+            return convert_unary_cuda<float>;
+        case GGML_TYPE_F16:
+            return convert_unary_cuda<half>;
+        default:
+            return nullptr;
+    }
+}
+
 to_fp16_cuda_t ggml_get_to_fp16_cuda(ggml_type type) {
     switch (type) {
         case GGML_TYPE_Q4_0:
@@ -633,6 +650,8 @@ to_fp16_cuda_t ggml_get_to_fp16_cuda(ggml_type type) {
             return dequantize_row_iq3_s_cuda;
         case GGML_TYPE_F32:
             return convert_unary_cuda<float>;
+        case GGML_TYPE_BF16:
+            return convert_unary_cuda<nv_bfloat16>;
         default:
             return nullptr;
     }
diff --git a/ggml/src/ggml-cuda/convert.cuh b/ggml/src/ggml-cuda/convert.cuh
index 5394be9f..411a13cf 100644
--- a/ggml/src/ggml-cuda/convert.cuh
+++ b/ggml/src/ggml-cuda/convert.cuh
@@ -7,7 +7,10 @@ using to_t_cuda_t = void (*)(const void * __restrict__ x, T * __restrict__ y, in
 
 typedef to_t_cuda_t<float> to_fp32_cuda_t;
 typedef to_t_cuda_t<half> to_fp16_cuda_t;
+typedef to_t_cuda_t<nv_bfloat16> to_bf16_cuda_t;
 
 to_fp16_cuda_t ggml_get_to_fp16_cuda(ggml_type type);
 
+to_bf16_cuda_t ggml_get_to_bf16_cuda(ggml_type type);
+
 to_fp32_cuda_t ggml_get_to_fp32_cuda(ggml_type type);
diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 86192765..060550c5 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -1194,7 +1194,35 @@ static void ggml_cuda_op_mul_mat_cublas(
 
     const bool use_fp16 = (src0->type == GGML_TYPE_F16 || ggml_is_quantized(src0->type)) && ggml_is_contiguous(src0) && row_diff == src0->ne[1] && dst->op_params[0] == GGML_PREC_DEFAULT;
 
-    if (((GGML_CUDA_CC_IS_NVIDIA(cc) && cc >= GGML_CUDA_CC_VOLTA) || GGML_CUDA_CC_IS_AMD(cc)) && use_fp16) {
+    if (src0->type == GGML_TYPE_BF16 && ggml_is_contiguous(src0) && row_diff == src0->ne[1]) {
+        ggml_cuda_pool_alloc<nv_bfloat16> src1_as_bf16(ctx.pool(id));
+        if (src1->type != GGML_TYPE_BF16) {
+            const to_bf16_cuda_t to_bf16_cuda = ggml_get_to_bf16_cuda(src1->type);
+            GGML_ASSERT(to_bf16_cuda != nullptr);
+            size_t ne = src1_ncols*ne10;
+            src1_as_bf16.alloc(ne);
+            to_bf16_cuda(src1_ddf_i, src1_as_bf16.get(), ne, stream);
+        }
+        const nv_bfloat16 * src1_ptr = src1->type == GGML_TYPE_BF16 ? (const nv_bfloat16 *) src1_ddf_i : src1_as_bf16.get();
+        const nv_bfloat16 * src0_ptr = (const nv_bfloat16 *)src0_dd_i;
+        ggml_cuda_pool_alloc<nv_bfloat16> dst_bf16(ctx.pool(id), row_diff*src1_ncols);
+
+        const float alpha_f32 = 1.0f;
+        const float beta_f32  = 0.0f;
+
+        CUBLAS_CHECK(cublasSetStream(ctx.cublas_handle(id), stream));
+        CUBLAS_CHECK(
+            cublasGemmEx(ctx.cublas_handle(id), CUBLAS_OP_T, CUBLAS_OP_N,
+                    row_diff, src1_ncols, ne10,
+                    &alpha_f32,  src0_ptr,       CUDA_R_16BF, ne00,
+                                 src1_ptr,       CUDA_R_16BF, ne10,
+                    &beta_f32,   dst_bf16.get(), CUDA_R_16BF, ldc,
+                    CUBLAS_COMPUTE_32F,
+                    CUBLAS_GEMM_DEFAULT_TENSOR_OP));
+
+        const to_fp32_cuda_t to_fp32_cuda = ggml_get_to_fp32_cuda(GGML_TYPE_BF16);
+        to_fp32_cuda(dst_bf16.get(), dst_dd_i, row_diff*src1_ncols, stream);
+    } else if (((GGML_CUDA_CC_IS_NVIDIA(cc) && cc >= GGML_CUDA_CC_VOLTA) || GGML_CUDA_CC_IS_AMD(cc)) && use_fp16) {
         // convert src0 and src1 to fp16, multiply as fp16, convert dst to fp32
         ggml_cuda_pool_alloc<half> src0_as_f16(ctx.pool(id));
         if (src0->type != GGML_TYPE_F16) {